Calculate the summations

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- September 18th 2012, 01:21 PMWORLDCalculate the summations
Calculate the summations

- September 18th 2012, 04:25 PMtopsquarkRe: Calculate the summations
How far have you been able to work these? And are these 4 questions?

-Dan - September 19th 2012, 09:36 AMWORLDRe: Calculate the summations
the firs problem

- September 19th 2012, 09:37 AMWORLDRe: Calculate the summations
the second problem

- September 19th 2012, 09:38 AMWORLDRe: Calculate the summations
the third problem

- September 19th 2012, 09:38 AMWORLDRe: Calculate the summations
the last problem

- September 19th 2012, 09:43 AMWORLDRe: Calculate the summations
till the farther far

- September 19th 2012, 11:52 AMPetrusRe: Calculate the summations
i would also intressted on how to solve this :D

- September 19th 2012, 09:49 PMtopsquarkRe: Calculate the summations
- September 19th 2012, 10:04 PMWORLDRe: Calculate the summations
It’s mean

- September 20th 2012, 11:41 PMWORLDRe: Calculate the summations
could any one help me

- September 22nd 2012, 05:12 PMawkwardRe: Calculate the summations
Hello, WORLD!

This is a tough problem for the algebra forum. I'm going to use a little calculus. I hope you will still find my remarks useful.

Start with the Binomial Theorem:

Integrate both sides from 0 to x (this is the calculus part). The result is

Now multiply these two equations together. I'm going to replace i with j in the first equation, so it will be easier to keep everything straight.

(*)....

Now consider the coefficient of in (*). The left-hand side of (*) is equal to

so the coefficient of is

On the right-hand side of (*), the coefficient of occurs when j = n-i, so the coefficient is

since .

The coefficient of must be the same on both sides of the equation, so we have

Now set n = 100, and you're done.