9. Sequences, Series, & Induction

The first 4 terms of a sequence are $\left\lbrace\sqrt3,2\sqrt3,3\sqrt3,4\sqrt3,\ldots\right\rbrace$. Continuing this pattern, find the $7^{\th}$ term.

Determine the first 3 terms of the sequence given by the general formula

$a_{n}=\frac{1}{n!+1}$

Write the first 6 terms of the sequence given by the recursive formula $a_{n}=a_{n-2}+a_{n-1}$ ; $a_1=1$ ; $a_2=1$.

Write the first four terms of each sequence whose general term is given. a_n=3n+2

Write the first four terms of each sequence whose general term is given. a_n = 7n - 4

Write the first four terms of each sequence whose general term is given. a_n=3ⁿ

Write the first four terms of each sequence whose general term is given. $a_n=1/(n-1)!$

Write the first four terms of each sequence whose general term is given. a_n=(−3)ⁿ

Evaluate $\frac{40!}{4!38!}$

Write the first four terms of each sequence whose general term is given. a_n=(−1)ⁿ(n+3)

In Exercises 8–9, find each indicated sum. This is a summation, refer to the textbook.

Write the first four terms of each sequence whose general term is given. a_n=2n/(n+4)

In Exercises 10–11, express each sum using summation notation. Use i for the index of summation. 1/3 + 2/4 + 3/5 + ... + 15/17

In Exercises 1–12, write the first four terms of each sequence whose general term is given. a_n=(−1)ⁿ⁺¹/(2ⁿ−1)

The sequences in Exercises 13–18 are defined using recursion formulas. Write the first four terms of each sequence. a₁=7 and a_n=a_n-1 + 5 for n≥2