Does the sequence $c_n=\frac{4n^2+1}{n^2+9}$ converge?

Find the limit of the sequence $\left\{m\tan \left(\frac{2}{m}\right)\right\}$ as $m\to \infty$.

Let $c_1=3$, and $c_{n+1}=\sqrt{3c_n}$. If the sequence converges, what is its limit?

What does the exclamation point (!) indicate when placed after a number in mathematics?

What is the value of 5! ?

Simplify the expression (n+1)! / n! for any positive integer n.

Find the sum of the geometric series $\sum _{n=0}^{\infty }{0.8}^n$, or indicate that the series diverges.

Consider the telescoping series $\sum _{k=1}^{\infty }\frac{1}{(k+1)(k+2)}$. Evaluate the series by finding the formula for the $n$^th term of the sequence of partial sums $\left\{S_n\right\}$, and by evaluating $\underset{n\to \infty }{\lim }{S}_n$.

Find the sum of the infinite series $\sum _{j=1}^{\infty }(\frac{6}{5^j}-\frac{6}{5^{j+1}})$ using a geometric series argument.

To apply the Comparison Test to $\sum _{m=1}^{\infty }\frac{1}{m^4+5}$, which series should you compare it with?

Does the series $\sum _{m=1}^{\infty }\frac{(-1{)}^{m+1}}{m}$ converge?

Consider the series $\sum _{m=1}^{\infty }\frac{(-1{)}^{m}m}{2m+1}$. Does this series converge?