SOLUTION: EVALUATE:
{{{1+3/4+7/16+15/64+31/256}}} ......... to infinity
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Question 537595: EVALUATE:
......... to infinity
Found 2 solutions by Edwin McCravy, AnlytcPhil:
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!
Answer by AnlytcPhil(1806) (Show Source): You can put this solution on YOUR website!
......... to infinity
Consider the first term as
......... to infinity
The numerators form the sequence 1,3,7,15,31
That has nth term
The denominators form the sequence 1,4,16,64,256
That has nth term
Therefore the sequence summed to infinity is
= - =
Subtract exponents in the first:
-
The first series diverges to infinity and the second one is a geometric
series converging to 2, so the series diverges to infinity.
Edwin
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