Question

Find the value of (1.01)⁵, correct upto three places of decimals.

Answer 1

(1.01)^5=1.0510100501=1.052
I hope it will help you....

Answer 2

Solution :

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By Binomial Theorem :

$\rm \displaystyle \left ( x + a )^n \right ) = ^nC_{r}x^{n}+^nC_{n}x^{n-1}a^{r}+..+ ^nC_{r}x^{n-r}a^{r}+...+^nC_{n}a^n$

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Here ,

$ ( 1.01 )^5 $

= $ ( 1 + 0.01 )^{5} $

= $\rm \displaystyle \left (1+0.1)^5 \right )= ^5C_{0}1^{5}+^5C_{1}1^{4}(0.01)^{4}+^{5}C_{2}(0.01)^{3}+^{5}C_{4}(0.01)^{4}+^{5}C_{5}(0.01)^5$

= $\rm \textsf { 1+5(0.01)+10(0.01)^2+10(0.01)^3+5(0.01)^4+1(0.01)^5 }$

= $ 1 + 0.05 + 0.001 + 0.000001 + 0.00005 + 0.0000000001 $

= 1.05101001501

≈ 1.051

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