$\prod_{k=1}^{100} ( k^2 /(k+1) )= 100!/101,$ right?

Question

$$\prod_{k=1}^{100}( k^2 /(k+1) )= (100!)^2/(101!) = (100!)^2/(101 * 100!) = 100!/101$$

is how I got my answer. Is that correct?

Answer 1

Your calculations are right !!!

$$\prod\limits_{k=1}^{100}\frac{k^2}{(k+1)}=(\prod\limits_{k=1}^{100}k^2)*\prod\limits_{k=1}^{100}\frac{1}{(k+1)}=\frac{(100!)^2}{101!}=\frac{100!}{101}$$