Write the statements P₁, P_k , and P_k+1 for the equation $1(1 !)+2(2 !)+\cdots+n(n !)=(n+1) !-1$ as if you were writing a proof by mathematical induction. Do not write a proof.

Name: Write the statements P 1 , P k , and P k+1 for the equation $1(1 !)+2(2 !)+\cdots+n(n !)=(n+1) !-1$ as if you were writing a proof by mathematical induction. Do not write a proof.
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Question

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The Answer is

\begin{array}{l}P_{1}=1(1 !)=2 !-1 \P_{k}=1(1 !)+2(2 !)+\ldots+k(k !)=(k+1) !-1 \P_{k+1} \=1(1 !)+2(2 !)+\ldots+k(k !)+(k+1)(k+1) ! \=(k+1) !-1+(k+1)(k+1) !\end{array}

Write the Statements P1, Pk , and Pk+1 1(1!)+2(2!)+⋯+n(n!)=(n+1)!−11(1 !)+2(2 !)+\cdots+n(n !)=(n+1) !-11(1!)+2(2!)+⋯+n(n!)=(n+1)!−1

Write the Statements P₁, P_k , and P_k+1 $1(1 !)+2(2 !)+\cdots+n(n !)=(n+1) !-1$