Question

prove by the principle of mathematical induction the sum of the first n non - zero even numbers is n²+n
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Answer 1

Answer:

Here, according to me, what is Required to prove that: (n² + n) always represents an even number, whether n is even or odd.

Step-by-step explanation:

Proof: If ‘n’ is an even number, (n+1) has to be odd. ( consecutive nos)

& if ‘n’ is an odd number, ( n+1) has to be even.

& we know that, the product of an odd & even is always an even .

=> n( n+1) = even

=> n² + n = even

(1) If n is even in the above, n² will be even too.

This way the sum of 2 non zero even numbers = n² + n , which is even.

(2) If n is odd , n² will be odd too.

So, the sum of 2 non zero odd numbers also = n² +n, which is even