Question

Let $P\left(n\right)=x^{2n-1}+y^{2n-1}$ is divisible by $x+y$ as $P\left(1\right)$ is true, then truth of $P(k+1)$ indicates

• A. $P\left(n\right)$ s divisible by $x+y$ only for odd positive integer
• B. $P\left(n\right)$ is divisible by $x+y$ only for positive even integer
• C. $P\left(n\right)$ is true $\forall n\in N$
• D. $P\left(k\right)$ is true

Answer 1

The correct option is C $P\left(n\right)$ is true $\forall n\in N$

This is the basic principle of mathematic induction that if P(1) is true and P(k+1) is true, then P(n) must be true $\forall n\in N$.