The part I've underlined is what I don't understand - where did the second (k+1) come from? Did the author make a substitution that I am not registering?
2026-04-01 04:41:57.1775018517
Induction proof - Stumped as to how a certain step was achieved
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Take a look at the indices of summation. On the LHS of the equation, it goes up to $k+1$, but on the RHS, it goes to $k$. The last term is brought out of the summation, which is what you underlined.