I am (somewhat) familiar with proving using induction, but why is proof of Bernoulli's inequality, after assuming validity for P(k), set for P(k+1) as:

I don't understand the right side of inequation, shouldn't it be:

I see that the inequality must be strictly multiplied by "(1+x)" onbothsides (in orderto remain the sameinequality), but shouldn't one, strictly following rules ofmathematical induction, insert "k+1" on both sides, and thus get