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Let S(k) = 1 + 3 + 5 +...+ (2k -1) = 3 +...

Let `S(k) = 1 + 3 + 5 +...+ (2k -1) = 3 + k^2`. Then which of the following is true ?

A

Principle of mathematical induction can be used to prove the formula

B

`S(k)rArr S(k+1)`

C

`S(k)cancelrArrS(k+1)`

D

S(1) is correct

Text Solution

Verified by Experts

We have `,S(k) =1+3+5+......+(2k-1)=3+k^2`,
`S(1)rArr 1=4`, which is not true
and `S(2)rArr =7`, which is not true.
Hence , induction cannot be applied and `S(k)ne S(k+1)`.
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