y_n := sqrt(n+1) - sqrt(n)

the question asks us to show that y_n and sqrt(n)*y_n converge and to find their limits

i can see that y_n would converge to 0, but i can't show how. i don't even know what the second converges to.

my strategy was to use the x_(n+1)/x_n theorem, but I was left with a messy equation whose comparison to 1 i can't illustrate.

at the very least i ask what theorem i should use. thanks.