Calculus 2

Determine if the sequence $A_n = \frac{N}{N+1}$ is convergent or divergent as $N \to \infty$.

Find the missing term in the sequence 2, 5, 10, _, 26 by identifying the pattern.

Find the missing term in the Fibonacci-like sequence 1, 2, 3, 5, 8, _, 21 where each term is the sum of the previous two terms.

Given the sequence $a_n = (-1)^n (n - 2)$, find the first five terms of the sequence.

Given the sequence $b_n = \frac{3n}{n+4}$, find the first five terms of the sequence and reduce if necessary.

Given the recursive sequence $c_0 = 2$ and $c_{n+1} = c_n + 4$, find the first five terms of the sequence.

Determine if the sequence $a_n = \frac{n-1}{n!}$ converges or diverges as $n \to \infty$.

Identify which convergence test to use for a geometric series involving terms like $\frac{2^n}{5^n}$.