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Question
Find the sum to n terms of the series 1 × 2 × 3 + 2 × 3 × 4 + 3 × 4 × 5 + …
Solution
The given series is 1 × 2 × 3 + 2 × 3 × 4 + 3 × 4 × 5 + …
nth term, an = n ( n + 1) ( n + 2)
= (n2 + n) (n + 2)
= n3 + 3n2 + 2n
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