Changing formula inside summation

Question

I probably forgot something about summations but can someone explain to me how do you go from $$ \sum_{n=-\infty}^\infty \delta(\frac{t}{2}-n) $$ to $$ 2\sum_{n=-\infty}^\infty \delta(t-2n) $$ Thanks

Answer 1

Using $\delta(ax) = \frac{1}{|a|}\delta(x)$ you get $$ \delta(\frac{t}{2}-n) = \delta(\frac12(t-2n)) = \frac{1}{1/2}\delta(t-2n) = 2\delta(t-2n). $$