Solve this: Q.195. The value of the infinite series 1 2 . 3 + 2 2 . 5 + 3 2 . 7 + 4 2 . 9 + . . . . . . . . is (a) 2 3 (b) 2e (c) e 2 (4) 1 2 e Share with your friends Share 0 Brijendra Pal answered this Hi, let I = 12×3+22×5+32×7+42×9+......∞2I = 13+25+37+49+.....∞now nth term of this series can be given as 1,2,3,4...in numerator has n as nth term and denominator has 3,5,7,9,.... it is AP with a = 3 and d = 2 so nth term = 3+n-12= 2n+1= n2n+1now this series limn→∞n2n+1 is a diverging series that do not converse meaning its sums cannot be calculated so please recheck the sum. 0 View Full Answer