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Question

The sum of the series 34·8-3·54·8·12+3·5·74·8·12·16-.......... is


A

32-34

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B

23-34

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C

32-14

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D

23-14

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Solution

The correct option is B

23-34


Explanation for the correct option

Given: 34·8-3·54·8·12+3·5·74·8·12·16-..........

Let, S=34·8-3·54·8·12+3·5·74·8·12·16-..........

add 1-14to both sides

S+1-14=1-14+34·8-3·54·8·12+3·5·74·8·12·16-..........S+34=1-11·14+1438-1438512+1438512716-........S+34=1-11·14+1·31·2142-1·3·51·2·3143+................

Let p=1,q=2,x=12

S+34=1-p1xq+p·p+q1·2xq2-p·p+q(p+2q)1·2·3xq3+............

expansion of (1+x)-pq=1-p1xq+p·p+q1·2xq2-p·p+q(p+2q)1·2·3xq3+............

S+34=(1+x)-pq

Put p=1,q=2,x=12

S+34=(1+12)-12S+34=32-1S+34=23S=23-34

Hence, OptionB is correct.


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