1*2 +2*(2^2)+2*(2^3)............+100*(2^100)

Question

Find the sum of series.

Answer 1

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

Now I think the beginning of your sequence should be

2*2^0 + 2*2^1 + 2*2^2 + ...

In that case, the sum is 2*(2^101-1)/(2-1)

Answer 2

On the other hand, there could be only one typo and the series is

1(2^1) + 2(2^2) + 3(2^3 + ... + 100(2^100)

In that case you have a hypergeometric series ...

Answer 3

I think I gotta go with Reiny. My answer is bogus because of the 100*2^100.

What was I thinking?