## Sum of order: 1*2 + 2*3+ 3*4+....+ 999*1000

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
japiga
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### Re: Sum of order: 1*2 + 2*3+ 3*4+....+ 999*1000

1^2+2^2+3^2…..+ 999^2 . How to put this sum in the simple mathematic formula? Since, only 999^2 = 998001and imagine total sum: + 998^2 + 997^2 + 996^2 + ... + 1. I hope that now is more clear what I actually need. Thanks a lot!

Martingale
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### Re: Sum of order: 1*2 + 2*3+ 3*4+....+ 999*1000

1^2+2^2+3^2…..+ 999^2 . How to put this sum in the simple mathematic formula? Since, only 999^2 = 998001and imagine total sum: + 998^2 + 997^2 + 996^2 + ... + 1. I hope that now is more clear what I actually need. Thanks a lot!
I've given you the formula for the sum of the squares of the first 999 natural numbers...ie

$1^2+2^2+3^2+\cdots+999^2$

If I say any more I will be giving you the answer..is that what you are wanting me to do?

japiga
Posts: 32
Joined: Mon Sep 20, 2010 3:28 pm
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### Re: Sum of order: 1*2 + 2*3+ 3*4+....+ 999*1000

Do you think that this assignment is finished if I accept this and moreover if my teacher accept it? Is there more mathematic approach and more predictable the final result of this “quadratic” sum? Since first sum (1+2+3+…+999) is more clear how to reach the final result!

Martingale
Posts: 333
Joined: Mon Mar 30, 2009 1:30 pm
Location: USA
Contact:

### Re: Sum of order: 1*2 + 2*3+ 3*4+....+ 999*1000

Do you think that this assignment is finished if I accept this and moreover if my teacher accept it? Is there more mathematic approach and more predictable the final result of this “quadratic” sum? Since first sum (1+2+3+…+999) is more clear how to reach the final result!
Sorry, but I really don't understand what you are trying to say.

I'll leave you with this..

if I wanted $1^2+2^2+3^2+\cdots+9^2$

I would use the formula $\frac{n(n+1)(2n+1)}{6}$ with $n=9$ to get

$\sum_{i=1}^{9}i^2=1^2+2^2+3^2+\cdots+9^2=\frac{9(9+1)(2\cdot9+1)}{6}=\frac{9\cdot10\cdot19}{6}=285$

japiga
Posts: 32
Joined: Mon Sep 20, 2010 3:28 pm
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### Re: Sum of order: 1*2 + 2*3+ 3*4+....+ 999*1000

Now, it's OK. I understood. It sounds very simple. Thanks a lot. This is great way of communication and very quick tool for maths problem solving! Be in touch. Regards