Principle Of Mathematical Induction Question 27
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 $
Correct Answer: 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) $
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Answer:
Solution:
$ \Rightarrow a(200)>100 $ and $ a(100)\le 100. $
BETA
