Math Is Fun Forum

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Sum of All Even Integers

For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum of all the even integers between 99 and 301?

A. 10,100
B. 20,200
C. 22,650
D. 40,200
E. 45,150

Can someone set this up for me?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: Sum of All Even Integers

sum of all the even integers between 99 and 301?

The formula works for sets of integers that do not have any gaps so use the fact that evens are involved to get a continuous sequence of integers. ie:

100 + 102 + ... + 300 = 2 x (50 + 51 + ... 150)

So find ∑49 and ∑150, subtract and then x2.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Sum of All Even Integers

sum of all the even integers between 99 and 301?

The formula works for sets of integers that do not have any gaps so use the fact that evens are involved to get a continuous sequence of integers. ie:

100 + 102 + ... + 300 = 2 x (50 + 51 + ... 150)

So find ∑49 and ∑150, subtract and then x2.

Bob

What do you mean by x2? Did you mean to type x^2?

Why must I subtract x2 or x^2 from the sum of
∑49 and ∑150?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: Sum of All Even Integers

I meant times by 2. Every even number is double an integer eg  100 = 2 times 50

Sometimes I type x for multiply.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Sum of All Even Integers

I meant times by 2. Every even number is double an integer eg  100 = 2 times 50

Sometimes I type x for multiply.

Bob

Sorry Bob but I'm still a bit confused. Can you start this one for me?

amnkb

Member

Registered: 2023-09-19

Posts: 253

Re: Sum of All Even Integers

For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum of all the even integers between 99 and 301?

Can someone set this up for me?

The formula works for sets of integers that do not have any gaps so use the fact that evens are involved to get a continuous sequence of integers. ie:

100 + 102 + ... + 300 = 2 x (50 + 51 + ... 150)

So find ∑49 and ∑150, subtract and then [multiply by] 2.

I'm still a bit confused. Can you start this one for me?

working from bob's start & using his steps:

Last edited by amnkb (2023-11-22 12:23:10)

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Sum of All Even Integers

For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum of all the even integers between 99 and 301?

Can someone set this up for me?

The formula works for sets of integers that do not have any gaps so use the fact that evens are involved to get a continuous sequence of integers. ie:

100 + 102 + ... + 300 = 2 x (50 + 51 + ... 150)

So find ∑49 and ∑150, subtract and then [multiply by] 2.

I'm still a bit confused. Can you start this one for me?

working from bob's start & using his steps:

I will need to ignore your reply moving forward. I am tired of clicking on rectangles to see the answer.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: Sum of All Even Integers

sologuitar

Your behaviour is becomong less and less acceptable. Let me try to explain so there's no misunderstanding..

(1) Each day, when I log in I see a long string of posts from you.  I find it very hard to remember which posts have been answered and which ones are still 'live'.  If I've given you help but it hasn't been enough to get you to your own answer I'll try to give more help, but, at the moment I'm getting lost in all the posts.

(2) Every time you respond to a post you quote the previous post.  That isn't helping either. It just increases the amount I have to wade through.  It is possible to respond without quoting the previous post. What would help is a dialogue consisting of the following:

(i) post asking for help on a question.

(ii) (a) response from you saying that's it, I've got it now or (b) please offer more help about ......

(iii) if (a) then the thread is finished if (b) then wait for additional help and go back to step (ii)

(3) amnkb has been trying to help you as well as me.  You were getting the whole solution from amnkb but you asked for this not to happen. I asked amnkb that whole solutions be hidden so you could still try to work it out for yourself. That is what is now happening! Each box is a hint and the 'contents' of the box is the answer you should have obtained for yourself.  That takes a lot of time to set up but gives you maximum help. It's exactly what you asked for.

So it is very ungenerous of you to say

I am tired of clicking on rectangles to see the answer.

If you want help you have to accept it in whatever form it is offered. If you don't like it then say nothing! You are coming close to being banned for upsetting other members and I have to keep the peace.

So how should you go forward from here?

Look at the hints offered by me and by  amnkb.  If it is enough for you, then say "thank you", and move on.  If it's not then say precisely what your problem is so someone can try to help. Stop being rude to the members who are giving up their time freely to help you.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Sum of All Even Integers

sologuitar

Your behaviour is becomong less and less acceptable. Let me try to explain so there's no misunderstanding..

(1) Each day, when I log in I see a long string of posts from you.  I find it very hard to remember which posts have been answered and which ones are still 'live'.  If I've given you help but it hasn't been enough to get you to your own answer I'll try to give more help, but, at the moment I'm getting lost in all the posts.

(2) Every time you respond to a post you quote the previous post.  That isn't helping either. It just increases the amount I have to wade through.  It is possible to respond without quoting the previous post. What would help is a dialogue consisting of the following:

(i) post asking for help on a question.

(ii) (a) response from you saying that's it, I've got it now or (b) please offer more help about ......

(iii) if (a) then the thread is finished if (b) then wait for additional help and go back to step (ii)

(3) amnkb has been trying to help you as well as me.  You were getting the whole solution from amnkb but you asked for this not to happen. I asked amnkb that whole solutions be hidden so you could still try to work it out for yourself. That is what is now happening! Each box is a hint and the 'contents' of the box is the answer you should have obtained for yourself.  That takes a lot of time to set up but gives you maximum help. It's exactly what you asked for.

So it is very ungenerous of you to say

I am tired of clicking on rectangles to see the answer.

If you want help you have to accept it in whatever form it is offered. If you don't like it then say nothing! You are coming close to being banned for upsetting other members and I have to keep the peace.

So how should you go forward from here?

Look at the hints offered by me and by  amnkb.  If it is enough for you, then say "thank you", and move on.  If it's not then say precisely what your problem is so someone can try to help. Stop being rude to the members who are giving up their time freely to help you.

Bob

1. I had no idea that posting a few questions is a problem.

2. No need to threaten banning me from the website.

3. Member amnkb never complained to me about my reply to his answers.

4. I will try to adhere to your rules while searching for another math forum.

e_jane_aran

Member

Registered: 2023-09-15

Posts: 10

Re: Sum of All Even Integers

1. I had no idea that posting a few questions is a problem.

Had you not promised almost two months ago that you would post no more than three questions per day? (https://www.mathisfunforum.com/viewtopic.php?pid=434726#p434726)

Did you not, just three days ago, issue a rule restricting the number of questions others may post in one day? (https://www.mathisfunforum.com/viewtopic.php?pid=435960#p435960)

2. No need to threaten banning me from the website.

Was there a need for you to threaten banning me from the website? (https://www.mathisfunforum.com/viewtopic.php?pid=435630#p435630)

Was there a need, two and a half years ago, to demand a ban on someone who wasn't even here? (https://www.mathisfunforum.com/viewtopic.php?id=26386)

3. Member amnkb never complained to me about my reply to his answers.

Did amnkb not apologize many times for having somehow offended you, asking you please to explain what s/he was doing wrong? Did you not then criticise amnkb for "saying sorry all the time"? (https://www.mathisfunforum.com/viewtopic.php?pid=435912#p435912)

Should not one attempt in general to subscribe to the standards one imposes on others? ("...with what judgment ye judge, ye shall be judged: and with what measure ye mete, it shall be measured to you again.")

Aside to Admin Bob: You seem to have developed, during your many orbits about our Sun, deep reserves of patience and kindness. Your character is one I aspire to.

---

"They are fast. Faster than you can believe. Don't turn your back. Don't look away. And most of all, don't blink." -the 10th Doctor

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Sum of All Even Integers

I have moved on beyond the current topic. I will not post here unless it is totally needed.

amnkb

Member

Registered: 2023-09-19

Posts: 253

Re: Sum of All Even Integers

Did amnkb not apologize many times for having somehow offended you, asking you please to explain what s/he was doing wrong? Did you not then criticise amnkb for "saying sorry all the time"?

ty
u & bob r rly nice <3