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

Then,

T_u = [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

∴ S_n = ∑ n³ + 3∑ n² + 2∑ n

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