9. Sequences, Series, & Induction

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

The sequences in Exercises 13–18 are defined using recursion formulas. Write the first four terms of each sequence. a₁=3 and a_n=4a_n-1 for n≥2

The sequences in Exercises 13–18 are defined using recursion formulas. Write the first four terms of each sequence. a₁=4 and a_n=2a_n-1 + 3 for n≥2

In Exercises 19–22, the general term of a sequence is given and involves a factorial. Write the first four terms of each sequence. a_n = n²/n!

In Exercises 19–22, the general term of a sequence is given and involves a factorial. Write the first four terms of each sequence. a_n=2(n+1)!

Evaluate each factorial expression. 17!/15!

Evaluate each factorial expression. 16!/2!14!