It is given that (1/14)+(1/24)+(1/34)+.... to ∞ =(π4/90) .Then (1/14)+(1/34)+(1/54)+....to∞ is eaual to .

Question

It is given that (1/14)+(1/24)+(1/34)+.... to ∞ =(π4/90) .Then (1/14)+(1/34)+(1/54)+....to∞ is eaual to . (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

x=(1/14)+(1/34)+(1/54)+ ldots to ∞ =((1/14)+(1/24)+(1/34)+ ldots to ∞)-((1/24)+(1/44)+⋅s to ∞) =(π4/90)-(1/16)((1/14)+(1/24)+(1/34)+⋅s to ∞)=(π4/90)-(1/16)⋅ (π4/90) =(π4/96).

Q. It is given that 141​+241​+341​+.... to ∞=90π4​ .Then 141​+341​+541​+....to∞ is eaual to ____.

x=141​+341​+541​+…to∞ =(141​+241​+341​+…to∞)−(241​+441​+⋯to∞) =90π4​−161​(141​+241​+341​+⋯to∞)=90π4​−161​⋅90π4​ =96π4​.

Q. It is given that $\frac{1}{1 ^{4}} + \frac{1}{2 ^{4}} + \frac{1}{3 ^{4}} + ....$ to $\infty = \frac{π ^{4}}{90}$ .Then $\frac{1}{1 ^{4}} + \frac{1}{3 ^{4}} + \frac{1}{5 ^{4}} + ....$ to $\infty$ is eaual to ____.