Principle Of Mathematical Induction | Don't Memorise

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[sarvarxyz]

How can we assume P(k) is true in inductive hypothesis? Isn't it the whole this we are trying to prove?

[attahiratto]

Please for the last Part of the Right hand side where it was = k+1([k+1]+1)
How did she arrive at
(K+1)(k+2)

[niceguy]

Just curios, why we chose K + 1 as our assumption?
I mean what about K + 2 will it still work?