Show that for each integer k 2 1J, if P(k) is true, then P(k + 1) is true: Let k be anyr integer with k 2 1, and suppose that HR} is true. In other words, suppose that 5k X We must show that P(k + 1) is true. P[k + 1) is given by the equality 5k+1= X Further, since 51: + 1 is a partial sum of a series, we can represent it as follows. (Enter your answers in terms of k.) 5 _S+ k+1 \"1' i' ((k+1]+1]! {(+1 = + ((k+ 1) + 1)! [k + 2)! Since this expression is he same as the expression given by P(k + 1}. PUC + l) is true. This completes the inductive step. [Thus both the baSJs and the Inductive steps have been proved, and so the proof by mathen'lstr'calr induction is complete]