Question

# The sum of first 9 terms of the series 131+13+231+3+13+23+331+3+5+…… is

A
71
B
96
C
142
D
192

Solution

## The correct option is D 96Given series is 131+13+231+3+13+23+331+3+5+…∞ Let Tn be the nth term of the given series. ∴Tn=13+23+33+……+n31+3+5+……+upto n terms ={n(n+1)2}2n2=(n+1)24 S9=∑9n=1(n+1)24=14(22+33+……+102)+124−124 =14[10(10+1)(20+1)6−1]=3844=96

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