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Question

23+43+63+83+....


Solution

23+43+63+83+....Let Tn be the nth term of this series.Then,Tn=(2n)3=8n3Let Sn be the sum to n terms of the given series; Then,Sn=nk18k3=8nk1k3=8[n(n+1)2]2=8×n2(n+1)24=2n2(n+1)2Hence,Sn=2n2(n+1)2


Mathematics
RD Sharma
Standard XI

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