First slide

Permutations

Question

If $P_{r}$ stands for ${}^{n}{P_{r}}$ then sum of the series $1 + P_{1} + 2 P_{2} + 3 P_{3} + \dots + n P_{n}$ is

Moderate

A

$(n + 1)!$
B

$P_{n + 1} - 1$
C

$P_{n - 1} + 1$
D

none of these

Solution

$\begin{array}{l} 1 + P_{1} + 2 P_{2} + 3 P_{3} + \dots + n P_{n} \\ = 1 + 1! + 2 (2!) + 3 (3!) + \dots + n (n!) \\ = 1 + \sum_{r = 1}^{n} [(r + 1) - 1] r! = 1 + \sum_{r = 1}^{n} {(r + 1)! - r!} \\ = 1 + (n + 1)! - 1! = (n + 1)! \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App