SOLUTION: (1+1/2)(1+1/4)(1+1/16)(1+1/256).........

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Question 1081650: (1+1/2)(1+1/4)(1+1/16)(1+1/256).........
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
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(1+1/2)(1+1/4)(1+1/16)(1+1/256).........
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Let P = %281%2B1%2F2%29%281%2B1%2F4%29%281%2B1%2F16%29%281%2B1%2F256%29+ellipsis.

Multiply both sides by 1-1%2F2  (which is 1%2F2, of course).

Use

%281-1%2F2%29%2A%281%2B1%2F2%29 = 1-1%2F4,

%281-1%2F4%29%2A%281%2B1%2F4%29 = 1-1%2F16,

%281-1%2F16%29%2A%281%2B1%2F16%29 = 1-1%2F256,

and so on INFINITELY MANY times . . . 


You will get %281%2F2%29%2AP = 1,   which implies  P = 2.


Answer.  P = 2.

Solved.