Binomial Theorem And Its Simple Applications Question 197
Question: The positive integer just greater than $ {{(1+0.0001)}^{10000}} $
Options:
A) 4
B) 5
C) 2
D) 3
Show Answer
Answer:
Correct Answer: D
Solution:
- [d] $ {{(1+0.0001)}^{10000}}={{( 1+\frac{1}{n} )}^{n}},n=10000 $
$ =1+n.\frac{1}{n}+\frac{n(n-1)}{2!}\frac{1}{n^{2}}+\frac{n(n-1)(n-2)}{3!}\frac{1}{n^{3}}+…. $
$ =1+1+\frac{1}{2!}( 1-\frac{1}{n} )+\frac{1}{3!}( 1-\frac{1}{n} )( 1-\frac{2}{n} )+…. $
$ <1+\frac{1}{1!}+\frac{1}{2!}+\frac{1}{3!}+…….+\frac{1}{(9999)!} $
$ =1+\frac{1}{1!}+\frac{1}{2!}+……\infty =e<3 $
BETA
