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Question

Find the sum of the following series to n terms :
13+33+53+73+....

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Solution

13+53+73+........+(2n1)3=8n31+6n12n2
Let the sum of upto n term of the series
S=8n312n2+6n18n2(n+1)2412n(n+1)(2n+1)6+6n(n+1)2n2n2(n+1)22n(n+1)(2n+1)+3n(n+1)n(n+1)(n)[2n(n+1)2(2n+1)+3]nn(n+1)[2x2+2n4n2+3]n(n2+n)[2n22n+1]n2x42x3+x2+2x32x2+nn(2x4x2).

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