9. Sequences, Series, & Induction

In Exercises 1–6, write the first four terms of each sequence whose general term is given. a_n = 1/(n - 1)!

In Exercises 1–12, write the first four terms of each sequence whose general term is given. an=(−3)^n

Evaluate 40!/(4! 38!)

In Exercises 1–12, write the first four terms of each sequence whose general term is given. an=(−1)^n(n+3)

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

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

The sequences in Exercises 13–18 are defined using recursion formulas. Write the first four terms of each sequence. a_1=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. a_1=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. a_1=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 = n^2/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)!

In Exercises 23–28, evaluate each factorial expression. 17!/15!

In Exercises 23–28, evaluate each factorial expression. 16!/2!14!