The sum to the infinite terms of the series (5/32 ⋅ 72)+(9/72 ⋅ 1 12)+(13/1 12 ⋅ 1 52)+.... is

Question

The sum to the infinite terms of the series (5/32 ⋅ 72)+(9/72 ⋅ 1 12)+(13/1 12 ⋅ 1 52)+.... is (A) (1/8) (B) (1/36) (C) (1/54) (D) (1/72)

Tardigrade Admin · Accepted Answer

Tk=(5 + (k - 1) 4/(3 + (k - 1) 4)2 (7 + (k - 1) 4)2) =(4 k + 1/(4 k - 1)2 (4 k + 3)2) =(1/8) (1/(4 k - 1)2) - (1/(4 k + 3)2) Sn=T1+T2+T3+....+Tn =(1/8) (1/32) - (1/72) + (1/72) - (1/1 12) + (1/1 12) - (1/1 52) + . . . . + (1/(4 n - 1)2) - (1/(4 n + 3)2) =(1/8) (1/32) - (1/(4 n + 3)2) S∈ fty= undersetn arrow ∈ ftyl i mSn=(1/8) (1/9) - 0 =(1/72)

Q. The sum to the infinite terms of the series $\frac{5}{3 ^{2} \cdot 7 ^{2}} + \frac{9}{7 ^{2} \cdot 1 1 ^{2}} + \frac{13}{1 1 ^{2} \cdot 1 5 ^{2}} + ....$ is

$\frac{1}{8}$

$\frac{1}{36}$

$\frac{1}{54}$

$\frac{1}{72}$

Q. The sum to the infinite terms of the series 32⋅725​+72⋅1129​+112⋅15213​+.... is

81​

361​

541​

721​

Q. The sum to the infinite terms of the series $\frac{5}{3 ^{2} \cdot 7 ^{2}} + \frac{9}{7 ^{2} \cdot 1 1 ^{2}} + \frac{13}{1 1 ^{2} \cdot 1 5 ^{2}} + ....$ is

$\frac{1}{8}$

$\frac{1}{36}$

$\frac{1}{54}$

$\frac{1}{72}$