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Question

Sum the series :
21/441/881/16161/32.... is equal

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Solution

Consider the given series.

21/4.41/8.81/16.161/32......

S=21/4.22/8.23/16.24/32......

S=2(1/4+2/8+3/16+4/32+.......)

S=21/4(1+2/2+3/4+4/8+.......)

Let

T=1+22+34+48+..... (Infinity AGP series with a=1, r=1/2, d=1)

Therefore,

T=a1r+dr(1r)2

T=1112+1×12(112)2

T=112+12(12)2

T=2+2=4

Therefore,

S=21/4×4

S=21=2

Hence, this is the answer.


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