Binomial Theorem And Its Simple Applications Question 62
Question: For a positive integer n, Let $ a(n)=1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+…+\frac{1}{(2^{n})-1}. $ Then
Options:
A) $ a(100)\le 100 $
B) $ a(100)>100 $
C) $ a(200)\le 100 $
D) $ a(200)<100 $
Show Answer
Answer:
Correct Answer: A
Solution:
- [a] It can be proved with the help of mathematical induction that $ \frac{n}{2}>a(n)\le n. $
$ \therefore \frac{200}{2}<a(200) $
$ \Rightarrow a(200)>100 $ and $ a(100)\le 100. $
BETA
