Mathemathic Problem Test for A1 and Ak A k plus1 Assignment

Question Description

Hi I need the complete induction for the following problem – I tried it myself but did not get far.
I tested for A(1) and it is true and did A(k) => A(k+1) but I need the proof (see in the picture I tried already but don’t know how to continue and if it is even right)

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