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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