I want to show that the series $$\sum_{k=1}^{\infty} \binom{\frac{1}{2}}{k} (-1)^k$$ converges. I'm fairly sure it converges to zero, but haven't been successful. Will the ratio test work?
How to find $\lim_{h\rightarrow 0}\frac{\sin(ha)}{h}$ without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...
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