Question

For the given statement Pn, write the statements P1, Pk, and Pk+1.
(2 points)

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

Answer 1

Ok, so I believe here they are stating that the statement \(P_n\) represents the sum of even numbers up to \(2n\)

Answer 2

so, to find \(P_1\) we set \(n=1\) which means it will be the sum of even numbers up to \(2*1=2\) and its value will be \(1(1+1)=2\).

Does that make sense?

Answer 3

yes it does

Answer 4

but do i put p1=2

Answer 5

yes, you could write it as:\[P_1=1(1+1)=2\]

Answer 6

because:\[P_n=n(n+1)\]

Answer 7

so, to find \(P_k\), just set \(n=k\)

Answer 8

so then 2=k

Answer 9

no, it would be more like:\[P_k=2+4+...+2k=k(k+1)\]

Answer 10

similarly, for \(P_{k+1}\) just set \(n=k+1\)

Answer 11

i.e. where ever you see an \(n\) just replace it with \(k+1\)

Answer 12

so then ( k + 1) × ( k + 2)

Answer 13

perfect! well done! :)

Answer 14

thanks

Answer 15

yw :)