Mathematical Induction: 1+2+3+...+n= n/2(n+1)

[cyberspace]

Prove that the sum of the first n positive integers is:
1+2+3+...+n= n/2(n+1)

Here are my steps so far:
-assume n=k
1+2+3...+k=k/2(k+1)
-assuming that one of the statements is true implies that the next statement is true, n=k+1
1+2+3...+k+k+1= k/2+1/2(k+2)

I'm not so sure about the second step. Thanks for the help!

 

[galactus]

Try adding n+1 to both sides and showing \(\displaystyle \frac{(n+1)(n+2)}{2}\)

\(\displaystyle \frac{n(n+1)}{2}+(n+1)=\frac{(n+1)(n+2)}{2}\)