If $S = (1 + 0.0001)^{1000}$ , then the value of $[S]$ is (where [.] is denotes greatest integer function)

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Solution

The correct option is A $1$
$S = (1 + 0.0001)^{1000} \Rightarrow S = {(1 + \frac{1}{10^{4}})}^{1000} \Rightarrow S = 1 +^{1000} C_{1} {(\frac{1}{10^{4}})}^{1} +^{1000} C_{2} {(\frac{1}{10^{4}})}^{2} + \dots + {(\frac{1}{10^{4}})}^{1000}$

We know that $S > 1$
$S < 1 + \frac{1}{10} + \frac{1}{10^{2}} + \dots \dots \infty \Rightarrow S < \frac{1}{1 - \frac{1}{10}} \Rightarrow S < \frac{10}{9}$

Hence, the value of $[S] = 1$

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If S=(1+0.0001)1000, then the value of [S] is (where [.] is denotes greatest integer function)

The correct option is A 1S=(1+0.0001)1000⇒S=(1+1104)1000⇒S=1+1000C1(1104)1+1000C2(1104)2+⋯+(1104)1000 We know that S>1 S<1+110+1102+⋯⋯∞⇒S<11−110⇒S<109 Hence, the value of [S]=1

If $S = (1 + 0.0001)^{1000}$ , then the value of $[S]$ is (where [.] is denotes greatest integer function)