The sum value of the series (3/4) +(5/36) +(7/144) +(9/400) + ...∞ is

Question

The sum value of the series (3/4) +(5/36) +(7/144) +(9/400) + ...∞ is (A)  1  (B)  2  (C)  32  (D)  0

Tardigrade Admin · Accepted Answer

Let S=(3/4)+(5/36)+(7/144)+(9/400)+ ldots∞ =(3/12⋅22)+(5/22 ⋅32)+(7/32 ⋅42)+(9/42 ⋅52)+ ldots∞ =(22-12/12⋅22)+(32-22/22⋅32)+(42-32/32 ⋅42)+(52 -42/42⋅52)+ ldots∞ =1-(1/22)+(1/22)-(1/32)+(1/32)-(1/42)+(1/42)-(1/52)+ ldots∞ =1

Q. The sum value of the series
$\frac{3}{4} + \frac{5}{36} + \frac{7}{144} + \frac{9}{400} + ...\infty$ is

$1$

$2$

$32$

$0$

Q. The sum value of the series 43​+365​+1447​+4009​+...∞ is

1

2

32

0

Let S=43​+365​+1447​+4009​+…∞ =12⋅223​+22⋅325​+32⋅427​+42⋅529​+…∞ =12⋅2222−12​+22⋅3232−22​+32⋅4242−32​+42⋅5252−42​+…∞ =1−221​+221​−321​+321​−421​+421​−521​+…∞ =1

Q. The sum value of the series
$\frac{3}{4} + \frac{5}{36} + \frac{7}{144} + \frac{9}{400} + ...\infty$ is

$1$

$2$

$32$

$0$