Question

let y_n = sqrt(n+1) - sqrt(n) for all n in N. Show that sqrt(n)y_n converges. Find the limit.

Answer 1

here is what i did: I found n^(1/2)y_n. then I multiplied by its conjugate and divided by its conjugate. I multiplied top and bottom by the largest degree of n. All of the remaining terms converged so the quaotient would converge and i got 1/2