Question

If an = n(n!), then Σar from r =1 to 100 is equal to
(1) 101!
(3) 101! - 1
(2) 100! - 1
(4) 101! + 1​

Answer 1

Answer:

Ans is 101!-1

Answer 2

$\sum_{r=1}^{100}a_r$

$\sum_{r=1}^{100}r(r!)$

$=\sum_{r=1}^{100} \left \{ (r+1)!-1 \right \}r!$

⇒ $\sum_{r=1}^{100}a_r=\sum_{r=1}^{100} \left \{ (r+1)!-r! \right \}$

⇒ $\sum_{r=1}^{100}a_r=(2!-1!)+(3!-2!)+(4!-3!)+...+(101!-100!)$

⇒ $\sum_{r=1}^{100} a_r=101!-1$