The sum of the first 9 terms of the series 1 /1 + 1 + 2 / 1 +3 + 1 + 2 + 3 / 1 + 3 + 5......... is:

Hare, t1=131

t2=13+231+3

t3=13+23+331+3+5

So, tn=13+23+....+n31+3+5+....+(2n-1)=(n(n+1)2)2n2[1+2n-1]

=2n2(n+1)24n2

=(n+1)24

So we have to find the value of

n=19tn=n=19(n+1)24=14n=19(n2+2n+1)

=14{n=19n2+2n=19n+n=191}

=14[9(9+1)(29+1)6+29(9+1)2+91]

=14[90196+90+9]

=14[285+99]

=14384=96

Hence the correct option is (B).i.e 96