Thread: show limit approaches 0

whats the proper way of showing that 1/(4n^2 + 1) goes to 0? when you have a n on both the top and the bottom you could just divide top and bottom by n. but could you do the same for this problem even though there isnt a n on the top to get (1/n^2) / (4 + 1/n^2) = 0/4 = 0?

Originally Posted by jeph

whats the proper way of showing that 1/(4n^2 + 1) goes to 0? when you have a n on both the top and the bottom you could just divide top and bottom by n. but could you do the same for this problem even though there isnt a n on the top to get (1/n^2) / (4 + 1/n^2) = 0/4 = 0?

Use the following theorem.

Theorem: Let {s_n} be a sequence of non-zero terms. Then, lim s_n = 0 if and only if lim 1/s_n = +oo.