First slide

Binomial theorem for positive integral Index

Question

$T h e p o s i t i v e i n t e g e r j u s t g r e a t e r t h a n {(1 + 0.0001)}^{1000} i s$

Moderate

A

4
B

5
C

2
D

3

Solution

$We know that \lim_{n \to \infty} {(1 + \frac{1}{n})}^{n} = e a n d 2 < e < 3$
$S u p p o s e t h a t n = 10000 H e n c e, 2 < {(1 + 0.0001)}^{10000} < 3 \Rightarrow 2 < 1 + 10000 \times 10^{- 4} + \frac{10000 \times 9999}{2} \times 10^{- 8} + . . . < 3 T h e r e f o r e, t h e 3 i s t h e p o s i t i v e i n t e g e r j u s t g r e a t e r t h a n {(1 + 0.0001)}^{10000} H e n c e, o p t i o n d i s t h e a n s w e r$

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