Evaluate this sum in terms of n (the number of terms):
1 2 4 8 16
S =  +  +  +  +  + .....
2 5 41 3,281 21,523,361
(In reply to
Using Charlie's idea (spoiler?) by Bob Smith)
The formula you give checks out if you change the power of 2 in the numerator to n+2 rather than n+1, if you're starting numbering with n=0. If starting numbering with n=1, then it's the power of 2 in the denominator that should change, from n+1 to just n. In any case, the power of 2 in the numerator should be one higher than the power of 2 in the denominator in order to get the sequence 1/2, 1/10, 1/410, 1/1345210, 1/28953440450810.

Posted by Charlie
on 20051221 15:54:00 