Help---question from Princeton GMAT Math Bible

[amyyoung999]

I encounter a very similiar question as this one from Princeton GMAT Math
Bible.
The instruction on the book using the formula to slove this question
Can any body teach me the formula.

the question is

1+2^2+3^2+4^2+.....................9^2+10^2=?

[EmilKhalikov]

1 + 2 + 3 + ... + n = n(n+1)/2
1^2 + 2^2 + ... + n^2 = n(n+1)(2n+1)/6
1^3 + 2^3 + ... + n^3 = ( n^2(n+1)^2 )/4

I cannot believe they would ask such question. If you do not remember the formulas, you are pretty much screwed because it is nearly impossible to figure out those formulas.

[amyyoung999]

Thank you very much!
I encountered this question when I took the test last month,and my friend
encountered the same question this week.

[EmilKhalikov]

Here is more:
1 + 3 + 5 + ... + (2n - 1) =n^2
2 + 4 + 6 + ... + 2n = n*(n+1)
1^2 + 3^2 + ... + (2n-1)^2 = n(4n^2 - 1)/3
1^3 + 3^3 + ... + (2n-1)^3 = n^2(2n^2 - 1)

Combining these formulas with the ones I posted earlier should help calculating various integer series

[amyyoung999]

Wow!You are an elite on Math.
You must hold a PH.D from department of Mathematics.
Thanx a lot!

[EmilKhalikov]

Lol no, I am Applied Math major and I am pretty good at it, so I figure I help other people. It's a good practice for me too.

[amitabhprasad]

@ amyyoung999
do you mean you go this test in GMATPrep questions ?

[amyyoung999]

This question is from Princeton GMAT Math Bible.
I relize that the questions on the Princeton GMAT Math Bible are much more difficult than the questions on GMATPREP.