Question

Please please please help me. Mathematical induction
For the given statement Pn, write the statements \(P_1, ~P_k,~ and~ P_{k+1}\)

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

Answer 1

@ganeshie8

Answer 2

@Callisto

Answer 3

You have \[\large P_n ~: ~2 + 4 + 6 + . . . + 2n = n(n+1) \]

Answer 4

does \(P_1\) just mean substitute 1 for n?

Answer 5

Yep!
\[\large P_1 ~: ~2 = 1(1+1) \]

Answer 6

oh ok :) what about \(P_k\)? I am completely confused on that one :/

Answer 7

simply replace \(n\) by \(k\)

\[\large P_k ~: ~2 + 4 + 6 + . . . + 2k = k(k+1)\]

Answer 8

\[\large P_{\heartsuit} ~: ~2 + 4 + 6 + . . . + 2\heartsuit = \heartsuit(\heartsuit+1)\]

Answer 9

you make this seem so simple...

Answer 10

You can guess \(P_{k+1}\)

Answer 11

and for \(P_{k+1}\) would it be \(k+1(k+1+1)\)?

Answer 12

P_(k+1) is a "statement", not just an expression

Answer 13

it should say some complete sentence

Answer 14

\(\large P_{k+1} ~: ~2 + 4 + 6 + . . . + 2k = k+1(k+1+1)\)?

Answer 15

try again, you should replace all "n" by "(k+1)"

Answer 16

\(\large P_{k+1} ~: ~2 + 4 + 6 + . . . + 2k = (k+1)((k+1)+1)\)

Answer 17

right side looks good, left side isnt..

Answer 18

ugh
\(\large P_{k+1} ~: ~2 + 4 + 6 + . . . + 2(k+1) = (k+1)((k+1)+1)\)
hopefully?

Answer 19

Thats it !

Answer 20

:O

Answer 21

yay!

Answer 22

yay!

Answer 23

Thank you so much! I have been stuck on that question for hours

Answer 24

yw:) principle of induction is pretty interesting topic.. i hope they let you do some induction proofs as well !