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CBSE Class 10 Answered

It is known that 81 / 1 square + 1/2 square + 1 / 3 square +.......n =             π square/6 Then find the value of the series 1/       1 square + 1 / 3 square + 1 / 5 square +.......n
Asked by sujatha.vkthakur.21 | 29 Sep, 2019, 12:46: AM
answered-by-expert Expert Answer
G i v e n colon space 1 over 1 squared plus 1 over 2 squared plus... space equals space straight pi squared over 6
rightwards double arrow space open parentheses 1 over 1 squared plus 1 over 3 squared plus... close parentheses space plus open parentheses 1 over 2 squared plus 1 over 4 squared plus.... close parentheses equals space straight pi squared over 6
rightwards double arrow space open parentheses 1 over 1 squared plus 1 over 3 squared plus... close parentheses space plus 1 over 2 squared open parentheses 1 over 1 squared plus 1 over 2 squared plus.... close parentheses equals space straight pi squared over 6
rightwards double arrow 1 over 1 squared plus 1 over 3 squared plus 1 over 5 squared plus..... space equals space straight pi squared over 6 minus 1 over 2 squared open parentheses 1 over 1 squared plus 1 over 2 squared plus.... close parentheses
rightwards double arrow 1 over 1 squared plus 1 over 3 squared plus 1 over 5 squared plus..... space equals space straight pi squared over 6 minus 1 over 2 squared open parentheses straight pi squared over 6 close parentheses
rightwards double arrow 1 over 1 squared plus 1 over 3 squared plus 1 over 5 squared plus..... space equals space straight pi squared over 6 minus straight pi squared over 24 equals fraction numerator 3 straight pi squared over denominator 24 end fraction equals straight pi squared over 8
H e n c e comma space 1 over 1 squared plus 1 over 3 squared plus 1 over 5 squared plus..... space equals straight pi squared over 8
Answered by Renu Varma | 03 Oct, 2019, 11:07: AM
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