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Question

Write the sum of the series 2+4+6+8+...+2n.


Solution

Let Tn be the given series and S_nbe the sum of the given series.Tn=2nSn=nk1Tk=nk12k=2nk1k=2[n(n+1)2]=n(n+1)Hence,Sn =n(n+1)

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