SOLUTION: not very sure if this is in logic but I need some proof. I need to prove that this sequence {{{1+3+5+7+...}}} ends in {{{n^2+2n-1)}}} any help is very much appreciated than

Algebra ->  Proofs -> SOLUTION: not very sure if this is in logic but I need some proof. I need to prove that this sequence {{{1+3+5+7+...}}} ends in {{{n^2+2n-1)}}} any help is very much appreciated than      Log On


   

Question 994880: not very sure if this is in logic but I need some proof.
I need to prove that this sequence 1%2B3%2B5%2B7%2B... ends in n%5E2%2B2n-1%29
any help is very much appreciated
thanks
Found 2 solutions by Edwin McCravy, ikleyn:
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
That's false.  The sequence

1%2B3%2B5%2B7%2B... ends in 2n-1%29

Edwin

Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.
1 + 3 = 4,

1 + 3 + 5 = 9,

1 + 3 + 5 + 7 = 16,

1 + 3 + 5 + 7 + 9 = 25,

and so on.  Thus every time you get the sum equal to the square of an integer number.

So yours formula is wrong.

The correct formula is

1 + 3 + 5 + 7 + 9 + . . . + (2n-1) = n%5E2.

For the proof see the lesson  Mathematical induction and arithmetic progressions  in this site.