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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

AI Generated Solution

To solve the problem, we need to verify the statement given by \( S(k) = 1 + 3 + 5 + \ldots + (2k - 1) = 3 + k^2 \) using mathematical induction. ### Step 1: Base Case We start by checking the base case for \( k = 1 \). - **Left-hand side (LHS)**: \[ S(1) = 1 ...
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