Binomial Theorem And Its Simple Applications Question 87
Let $ S(k)=1+3+5…+(2k-1)=k^{2}. $ Then which of the following is true-
Options:
A) Principle of mathematical induction can be used to prove the formula
B) $ S(k)\Rightarrow S(k+1) $
C) $ S(k)\not{\Rightarrow }S(k+1) $
D) $ S(1) $ is correct
Show Answer
Answer:
Correct Answer: B
Solution:
- [b] $ S(k)=1+3+5+…+(2k-1)=k^{2} $
$ S(1):1=3+1, $ which is not true $ \because ,S(1) $ is false $ \therefore $ P.M.I cannot be applied Let S(k) be true, i.e, $ 1+3+5…+(2k-1)=k^{2}+3 $
$ \Rightarrow 1+3+5…+(2k-1)+2k+1 $
$ =3+k^{2}+2k+1=3+{{(k+1)}^{2}} $
$ \therefore S(k)\Rightarrow S(k+1) $
BETA
