Questions
The sum to n terms of the series is given by
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a
n2
b
n(n+1)
c
n(1+1/n)2
d
none of these
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Correct option is A
Let S be the sum of n terms of the given series and d x =1+1/n. Then, S=1+2x+3x2+4x3+…+nxn−1⇒xS=x+2x2+3x3+…+(n−1)xn−1+nxn∴S−xS=1+{x+x2+…+xn−1}−nxn⇒S(1−x)=1−xn1−x−nxn⇒S(−1/n)=−n[1−(1+1/n)n]−n(1+1/n)n⇒1nS=n{1−(1+1/n)n+(1+1/n)n}=n⇒S=n2Similar Questions
The positive integer n for which is
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