Question

find the sum of n termsin the series
1.2+2.3+3.4+.............(n-1)n

Answer 1

The series is 1.2 + 2.3 + 3.4 + .....+ (n-1)n + n(n+1)
From the given series, the nth term is n(n+1) or (n² + n)

Sum of first n terms of a series with nth term (n² + n) = Sum of first n terms of a series with nth term (n²) + Sum of first n terms of a series with nth term (n)

$= \frac{n(n+1)(2n+1)}{6} + \frac{n(n+1)}{2} \\ \\ = \frac{n(n+1)(2n+1)+3n(n+1)}{6} \\ \\ = \frac{n(n+1)[(2n+1)+3]}{6} \\ \\ = \frac{n(n+1)(2n+4)}{6} \\ \\ = \frac{n(n+1)(n+2)}{3}$

Answer 2

Answer:

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