Question

I have to know the correct statement for the formula 2+4+6...+2n=n(n+1) and show the formula true for n=k+1

Answer 1

is it true for n=1 ?

Answer 2

It is true for n=k, but it doesn't say anything about being true for n=1, so I assume so

Answer 3

dont assume; test it out

does 2n = n(n+1) when n=1? we have to establish this basis point as true before we can suggest that its true for the n=1+1

Answer 4

It does in this case

Answer 5

the we know that it is true for some n=k, particularly for n=k=1; so rewrite it in terms of k

1+2+3+...+2k = k(k+1)

Answer 6

I got that far but have no clue what so ever to do from there

Answer 7

now we simply have to add (k+1) to each side and see if we can get it into (k+1)(k+1+1) form

Answer 8

well, add 2(k+1) that is since thats the "next" value

Answer 9

makes sense

Answer 10

1+2+3+...+2k + 2(k+1) = k(k+1) + 2(k+1)

Answer 11

work the right side there so that it shows: \[[k+1] ~[( k+1)+1]\cong k~(k+1)\]

Answer 12

thank you so much that was so helpful Induction makes almost no sense to me. this helped a bunch thans

Answer 13

you are essentially saying that you know the format works for some n=k, specifically for k=1; and establishing that the (k+1)th term fits the same format ....