# Simplify the Following and Express with Positive Index : 1 - { 1 - ( 1 - N )^-1}^-1^-1 - Mathematics

Sum

Simplify the following and express with positive index :
[ 1 - { 1 - ( 1 - n )^-1}^-1]^-1

#### Solution

[ 1 - { 1 - ( 1 - n )^-1}^-1]^-1

= 1/[ [1 - { 1 - ( 1 - n )^-1 }^-1]^+1

= 1/[1 - 1/( 1 - ( 1 - n )^-1)]

= 1/[1 -  1/(1 -  1/( 1 - n ))]

= 1/[ 1 - ( 1 /( 1( 1 - n ) - 1 ))/( 1 - n )]

= 1/[ 1 - ( 1/-n)/( 1 - n )]

= 1/[ 1 - (1 - n)/-n ]

= 1/[ 1 + ( 1 - n )/n ]

= 1/[ (n + ( 1 - n ))/n ]

= [1/( n + 1 - n )]/n

= n/1

= n

Concept: Laws of Exponents
Is there an error in this question or solution?

#### APPEARS IN

Selina Concise Mathematics Class 9 ICSE
Chapter 7 Indices (Exponents)
Exercise 7 (A) | Q 4.4 | Page 98