Question

For every positive integer, prove that 1+2+...+n= n(n+1)/2

Answer 1

Inductive proof, maybe?

Answer 2

or try reversing the sequence and then adding it to itself, i.e.

1 + 2 + 3 + ... + n
n + (n-1) + (n-2) + ... + n
-----------------------

Answer 3

you may spot a pattern

Answer 4

sorry - small mistake:

or try reversing the sequence and then adding it to itself, i.e.

1 + 2 + 3 + ... + n
n + (n-1) + (n-2) + ... + 1
-----------------------

Answer 5

if n=2, then n(n+1)/2 = 2(3)/2=3 and 1 + 2 =3

Now assume it hold for k, so the 1+2+....+k=k(k+1)/2

Then show it for k+1, using the result for n=k.

Answer 6

@kdekle - you now have two methods to try out - take your pick! :)

Answer 7

Or better yet... prove it twice! :)

Answer 8

he he - too true @DebbieG :)

Answer 9

so @DebbieG, I should do like Induction to prove that this is correct?