I would love to show ANY effort of my own, but it seams to me that I should use some theorem (of which I have never heard of) in order to attack this problem.

Help, please!

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- Sep 19th 2011, 01:03 AMwitek123simplify: (x+1/x) + (x^2 + 1/x^2)^2 +...+(x^n + 1/x^n)^n
I would love to show ANY effort of my own, but it seams to me that I should use some theorem (of which I have never heard of) in order to attack this problem.

Help, please! - Sep 19th 2011, 04:11 AMislamRe: simplify: (x+1/x) + (x^2 + 1/x^2)^2 +...+(x^n + 1/x^n)^n
hello there notice that u can seperate this sequence

into two sequences which are both geometric

the first is:x+x^2+x^3+...........+x^n

the second is:1/x +1/x^2+1/x^3+.........1/x^n

now just use the formula for the sum of ageometric sequence - Sep 19th 2011, 04:26 AMPlatoRe: simplify: (x+1/x) + (x^2 + 1/x^2)^2 +...+(x^n + 1/x^n)^n
- Sep 19th 2011, 04:58 AMislamRe: simplify: (x+1/x) + (x^2 + 1/x^2)^2 +...+(x^n + 1/x^n)^n
sorry very sorry

i just missed the exponent - Sep 20th 2011, 01:38 AMwitek123Re: simplify: (x+1/x) + (x^2 + 1/x^2)^2 +...+(x^n + 1/x^n)^n
I'm starting to think the whole problem was a typo, and the real form should be:

(x+1/x) + (x^2 + 1/x^2) +...+(x^n + 1/x^n)

so it's quite simple.

But thanks for the help! - Sep 20th 2011, 03:47 AMPlatoRe: simplify: (x+1/x) + (x^2 + 1/x^2)^2 +...+(x^n + 1/x^n)^n