Practice Problem 2

Probability Level 2

1 P 1 + 2 . 2 P 2 + 3 . 3 P 3 + ⋯ + 10 . 10 P 10 = ? ^{1}\textrm{P}_{1} + 2.^{2}\textrm{P}_{2} + 3.^{3}\textrm{P}_{3} + \cdots + 10.^{10}\textrm{P}_{10} = ?

Try out other JEE problems!

11! 10! * 100 11! - 2! 11! - 1 12!

Vatsalya Tandon by Vatsalya Tandon , 21, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Vatsalya Tandon
Dec 16, 2015

= 1 P 1 + 2 . 2 P 2 + 3 . 3 P 3 + ⋯ + 10 . 10 P 10 = ^{1}\textrm{P}_{1} + 2.^{2}\textrm{P}_{2} + 3.^{3}\textrm{P}_{3} + \cdots + 10.^{10}\textrm{P}_{10} = 1 ! + 2.2 ! + ⋯ + 10.10 ! = 1! + 2.2! + \cdots + 10.10! = ( 2 − 1 ) 1 ! + ( 3 − 1 ) . 2 ! + ⋯ + ( 11 − 1 ) . 10 ! = (2-1)1! + (3-1).2! + \cdots + (11-1).10! = ( 2 ! − 1 ! ) + ( 3 ! − 2 ! ) + ( 4 ! − 3 ! ) + ⋯ + ( 11 ! − 10 ! ) = (2! - 1!) + (3! - 2!) + (4! - 3!) + \cdots + (11! - 10!) 11 ! − 1 \boxed{11! - 1}

6 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...