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Question

The sum of the first n terms of the series
12+34+78+1516+ is equal to ___.


A

n+2n1

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B

2nn1

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C

2n+1.

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D

12n

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Solution

The correct option is A

n+2n1


Let S=12+34+78+1516+n terms.i.e., S=(112)+(114)+(118)+(1116)n terms =(1+1+1+n terms)(12+122+123+124++12n)
The sequence 12,122,123,124,,12n forms a GP with first term a=12 and common ratio r=12.
The sum to n terms of a GP with first term a and common ratio r is
Sn=a(1rn)1r.
S =n[12(112n)112]=n1+2n


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