Question

The terms of a sequence {xn}∞ n=1
are not known exactly although it can be said
that ∀n −n < xn < n. Prove that yn = xn/n^2
converges

Answer 1

Hint: If \[-n <x_n<n\]Then dividing by n^2 yields:\[-\frac{1}{n} <\frac{x_n}{n^2} <\frac{1}{n}\]

Answer 2

\[x+y+z /3\ge \sqrt[3]{xyz}\]