10. Sequences, Induction, and Probability

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

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

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

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 29–42, find each indicated sum. 6Σi=1 5i

In Exercises 29–42, find each indicated sum. 9Σi=5 11

In Exercises 43–54, express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. 2+2^2+2^3+⋯+ 2^11

In Exercises 43–54, express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. 1+3+5+⋯+ (2n−1)

In Exercises 61–68, use the graphs of and to find each indicated sum.

5Σi=4 (a_i/b_i)^2

In Exercises 81–85, use a calculator's factorial key to evaluate each expression. 200!/198!

In Exercises 81–85, use a calculator's factorial key to evaluate each expression. 54!/(54−3)!3!

Write the first five terms of the sequence whose first term is 9 and whose general term is an= (an−1)/2 if a_n-1 is even, a_n=3a_n-1 + 5 if a_n-1 is odd for n≥2.

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+1/(2^n−1)

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 23–28, evaluate each factorial expression. (n+2)!/n!

In Exercises 29–42, find each indicated sum. 4Σi=1 (−1/2)^i

In Exercises 43–54, express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. 1^2+2^2+3^2+⋯+ 15^2

In Exercises 43–54, express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. 4+4^2/2+4^3/3+⋯+ 4^n/n

In Exercises 55–60, express each sum using summation notation. Use a lower limit of summation of your choice and k for the index of summation. a+(a+d)+(a+2d)+⋯+ (a+nd)

In Exercises 61–68, use the graphs of and to find each indicated sum.

5Σi=1 (a_i+3b_i)

In Exercises 61–68, use the graphs of and to find each indicated sum.

5Σi=1 a_i^2−5Σi=3 b_i^2

In Exercises 81–85, use a calculator's factorial key to evaluate each expression. 20!/(20−3)!

In Exercises 1–12, write the first four terms of each sequence whose general term is given. an=3n+2

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=2n/(n+4)

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

In Exercises 29–42, find each indicated sum. 5Σk=1 k(k+4)

In Exercises 29–42, find each indicated sum. 5Σi=1 i!/(i−1)!

In Exercises 43–54, express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. 1/2+2/3+3/4+⋯+ 14/(14+1)

In Exercises 55–60, express each sum using summation notation. Use a lower limit of summation of your choice and k for the index of summation. a+ar+ar2+⋯+ ar^12

In Exercises 61–68, use the graphs of and to find each indicated sum.

5∑i=1 (2a_i+b_i)

In Exercises 61–68, use the graphs of and to find each indicated sum.

5Σi=1 a_i^2+5Σi=1 b_i^2

In Exercises 81–85, use a calculator's factorial key to evaluate each expression. 20!/300

In Exercises 1–6, write the first four terms of each sequence whose general term is given. a_n = 7n - 4

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

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

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

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

In Exercises 29–42, find each indicated sum. 4Σi=1 2i^2

In Exercises 29–42, find each indicated sum. 4Σi=0 (−1)^i/i!

In Exercises 43–54, express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. 1+2+3+⋯+ 30

In Exercises 55–60, express each sum using summation notation. Use a lower limit of summation of your choice and k for the index of summation. 5+7+9+11+⋯+ 31

In Exercises 61–68, use the graphs of and to find each indicated sum.

5Σi=1 (a_i^2+1)

In Exercises 61–68, use the graphs of and to find each indicated sum.

5Σi=4 (a_i/b_i)^3

In Exercises 81–85, use a calculator's factorial key to evaluate each expression. (300/20)!