Question:
$$\text{Prove by induction that, for all integers } n, n \geq 1:$$ $$\sum\limits_{r=1}^{n} r >\frac{1}{2}n^2$$
Working:
Step 1 (Prove true for n=1): $$1>\frac{1}{2}(1)^2$$
Step 2 (Assume true for n=k): $$ k >\frac{1}{2}k^2$$
Step 3 (Prove true for n=k+1):
And having only faced equations with an equals (=) sign I have no idea what to do next. Right now I have assumed that it stands true for $k$ and I will try to prove for $k+1$. What should be my next step?