Q. 65

Find the sum of the following series upto n terms:1 × 2 + 2 × 3 + 3 × 4 + 4 × 5+……



Answer :


Let Tn denotes the nth term of the given series

Tn = [nth term of 1, 2, 3 …..] × [nth term of 2, 3, 4 …..]

    = [1 + (n – 1) 1] [2 + (n – 1) 1]

    = n(n + 1)

Tn = n2 + n

Sn = ∑ n2 + ∑ n

    =

    =

    =
    =
    =
    =

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