proof by induction

thank you for the detailed explanation

can you explain why you did Ur + U n+1 at the first part of ii please its the only part i didnt catch on to

"can you explain why you did Ur + U n+1 at the first part of ii please "

Think of the summation as follows:  \(\sum_{k=1}^nu_k=u_1+u_2+...+u_n\)

Hence \(\sum_{k=1}^{n+1}u_k=u_1+u_2+...+u_n+u_{n+1}\)  which is \(\sum_{k=1}^{n+1}u_k=\sum_{k=1}^nu_k+u_{n+1}\)

Hope that makes it clear.

perfect! i forgot about that haha thank you