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It is given that 1/14 + 1/24 + 1/34 + ......∞ = π4/90 then, |+ 1/34 + 1/54 + ........ ∞(a) π4/96(b) π4/45(c) 89π4/90(d) None of these |
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Answer» Correct option (a) π4/96 Explanation: Let 1/14 + 1/34 + 1/54 + .... ∞ = S Now 1/14 + 1/24 + 1/34 + ......∞ = π4/90 (1/14 + 1/34 + 1/54 + ....) + (1/24 + 1/44 + 1/64 + ...) = π4/90 ⇒ S + 1/24 (1/14 + 1/24 + 1/34 + ........ ∞) = π4/90 ⇒ S + 1/16 .π4/90 = π4/90 ⇒ S = π4/90(1 - 1/16) = π4/90 x 15/90 = π4/96 |
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