Question

Help please!

Answer 1

for the given statement Pn, write the statements P1, Pk, and Pk+1.
2+4+6...+2n=n(n+1)

Answer 2

induction

Answer 3

Yes I am aware of what type of problem it is.

Answer 4

well

Answer 5

Well I do not know what to do to get them into the different statements.

Answer 6

hmm

Suppose the equation is true for n = k

Just replace n by k.

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

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After you replace k by k+1, you get :

2 + 4 + 6 + ... + 2 × (k + 1) = k+1 ( k + 1 + 1)

2 + 4 + 6 + ... + 2 × ( k + 1) = k+1 ( k + 2)

2 + 4 + 6 + ... + 2 × ( k + 1) = ( k + 1 ) × ( k + 2)
Add 2 × ( k + 1) to both sides of the hypothesis

2 + 4 + 6 + ... + 2k + 2 × ( k + 1) = k ( k + 1) + 2 × ( k + 1)

= k2 + k + 2k + 2

= k2 + 3k + 2
Since 2 = 1 × 2 and 1 + 2 = 3,

k2 + 3k + 2 = ( k + 1) × ( k + 2)

Therefore, 2 + 4 + 6 + ... + 2k + 2 × ( k + 1) = ( k + 1) × ( k + 2) and the proof by mathematical induction

Answer 7

So you just replace n with whatever the value by P is? so like n=1, n=k, n=k+1? And then solve?

Answer 8

yes
in induction
u first prove for n=1
then n=k
then n=k+1

Answer 9

Okay and how do you get the value of the left side? you plug 1 into the n spot like 2n you would get 2? because I've watched this video: http://www.youtube.com/watch?v=IFqna5F0kW8 and I do not get how to get the left side value.

Answer 10

LOL
for n=1
n(n+1) = 1(1+1)=2
n is the number of terms
on left side
1st term
that means 2

Answer 11

Okay so for my problem there are 3 terms or do you count 2n?

Answer 12

rephrase it pls?

Answer 13

For my problem, the left side is 2+4+6+...+2n. Are there 3 terms or do you count 2n as a term on the left side?

Answer 14

nope
let me explain
for n=1 its 2(1) =
for n(2) its 2(2)=4
and 2n is written for nth term

Answer 15

sorry
its for n=2

Answer 16

so for nth term its 2*n

Answer 17

Okay so if I solve it for n=1 it would look like
2=1(1+1)
2=1(2)
2=2

Answer 18

how are you suppossed to solve for k?

Answer 19

Just replace n by k.

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

Answer 20

i told u the process
check it

Answer 21

I actually think you did something incorrect... I think it should be

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

Answer 22

that's for k+1

Answer 23

i have solved correctly