# Evaluate the (Viii) ( 0 . 99 ) 5 + ( 1 . 01 ) 5 - Mathematics

Evaluate the

(viii)  $\left( 0 . 99 \right)^5 + \left( 1 . 01 \right)^5$

#### Solution

$(0 . 99 )^5 + (1 . 01 )^5$
$= (1 - 0 . 01 )^5 + (1 + 0 . 01 )^5$
$= 2[ ^{5}{}{C}_0 (0 . 01 )^0 + ^{5}{}{C}_2 (0 . 01 )^2 + ^{5}{}{C}_4 (0 . 01 )^4 ]$
$= 2[1 + 10 \times 0 . 0001 + 5 \times 0 . 00000001]$
$= 2 \times 1 . 00100005 = 2 . 0020001$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 18 Binomial Theorem
Exercise 18.1 | Q 2.08 | Page 11