The sum of n terms of the series whose n t h term is n(n+1) is equal to Options: A . &nbsp n ( n + 1 ) ( n + 2 ) 3 B . &nbsp ( n + 1 ) ( n + 2 ) ( n + 3 ) 12 C . &nbsp n 2 (n+2) D . &nbsp n(n+1)(n+2)

Answer: Option A : A T π = n 2 + n ⇒ S π = ∑ T π = ∑ n 2 + ∑ n = n ( n + 1 ) ( 2 n + 1 ) 6 + n ( n + 1 ) 2 = n ( n + 1 ) 6 {2n + 1 + 3} = n ( n + 1 ) ( n + 2 ) 3

The sum of n terms of the series whose nth term is n(n+1) is equal

Discussion Forum : Sequences And Series

Question -

The sum of n terms of the series whose $n^{t h}$ term is n(n+1) is equal to

Options:

A .

\frac{n (n + 1) (n + 2)}{3}

B .

\frac{(n + 1) (n + 2) (n + 3)}{12}

C .

n^{2}

(n+2)

D . n(n+1)(n+2)

Answer: Option A
:
A

$T_{π}$ = $n^{2}$ + n ⇒ $S_{π}$ = $\sum T_{π}$ = $\sum$ $n^{2}$ + $\sum$ n

= $\frac{n (n + 1) (2 n + 1)}{6}$ + $\frac{n (n + 1)}{2}$

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

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