Question

For the given statement Pn, write the statements P1, Pk, and Pk+1.

2 + 4 + 6 + . . . + 2n = n(n+1)

Answer 1

it just means to substitute n =1, n = k and n = k + 1 into the right hand side.

\[P_{1} = 1\]

\[P_{k} = k(k +1)\]
\[P_{k + 1} = (k +1)(k+1+1)\]
= (k + 1)(k +2)

it looks a little bit like mathematical induction.