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Question

Find the sum of n terms of the series 21.545.7+87.171617.31+3231.65....

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Solution

When n is odd
un=2n(2n1)(2n+1)=13(12n1+12n+1)
And When n is even
un=2n(2n+1)(2n1)=13(12n+1+12n1)
3S2m=(11+15)(15+17)+(17+117).....(122m+1+1+122m+21)
and 3S2m+1=(11+15)(15+17)+.....+(122m+11+122m+2+1)
3S2m=1122m+11
3S2m+1=1+122m+1+1
3Sn=1+(1)n+12n+1+(1)n+1

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