Find the nth Partial Sum Sn of the series sum 1(2kappa −1)(2kappa +1) kindly solve fast.

slaggingV 2021-02-25 Answered
Find the nth Partial Sum Sn of the series
1(2κ1)(2κ+1)
kindly solve fast.
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Expert Answer

Obiajulu
Answered 2021-02-26 Author has 98 answers
k=1k=n1[(2k1)(2k+1)]
k=1k=n1[4(k2)1]
k=1k=n[4(k2)][1]
4k=1k=n[k2][1]
4(12)+22+32++n2)(1+2+3++n)
Sum of square of natural number =n(n+1)(2n+1)6
Sum of natural number =n(n+1)2
4n(n+1)(2n+1)6n(n+1)2
n(n+1)2×[4(2n+1)31]
n(n+1)2[8n+433]
n(n+1)2[8n+13]
n(n+1)(8n+1)6
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