Solve this: Q 195 The value of the infinite series 12 3+22 5+32 7+42 9+ - Maths - Sequences and Series

Question

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

Brijendra Pal · Accepted Answer

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

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

Solve this:
Q.195. The value of the infinite series
$\frac{1}{2.3} + \frac{2}{2.5} + \frac{3}{2.7} + \frac{4}{2.9} + . . . . . . . .$ is
(a) $\frac{2}{3}$
(b) 2e
(c) $\frac{e}{2}$
(4) $\frac{1}{2 e}$