Q. Prove that 1.3+2.4+3.5+....+n(n+2) = 1/6n (n+1) (2n+7),V nEN.

Hi!
Here is the proof to your question.
 
Let P (n): 1 × 3 + 2 × 4 + 3 × 5 + ... + n (n + 2)
Now, 1 × 3 = 3
Also,
 
∴P (k + 1) is true.
So, by method of induction it can be said that P (n) is true for n ε N
 
Hope! This will be helpful for you.
Cheers!!!

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