Q. 665.0( 5 Votes )

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

Let Tn denote the nth term of the given series .

Then,

Tu = [nth term of 1, 2, 3,….]

[nth term of 2, 3, 4,……]

[nth term of 3, 4, 5,……]

= [1 + (n – 1)1] [2 + (n – 1).1] [3 + (n –1).1]

= n(n + 1) (n + 2)

= n(n2 + 2n + 3) = n3 + 3n2 + 2n

∴ Sn = ∑ n3 + 3∑ n2 + 2∑ n

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