Posted by Anonymous on Friday, December 28, 2012 at 9:25am.
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)
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 ...
I think I gotta go with Reiny. My answer is bogus because of the 100*2^100.
What was I thinking?
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