Given is the series 1+2+3+4+5+...+n

Question

Show that n(n+1)\2

Answer 1

use induction.
P(1) is true, since 1 = 1(1+1)/2
So, assume P(k). Then consider the case for n=k+1
1+2+...+k+k+1 = k(k+1)/2 + k+1
Now show that that is the same as P(k+1): (k+1)(k+2)/2