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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`

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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
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APPEARS IN

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