9. Sequences, Series, & Induction

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

5Σi=4 (a_i/b_i)^2

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

5Σi=4 (a_i/b_i)^3

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 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. 200!/198!

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

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

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

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 11–24, use mathematical induction to prove that each statement is true for every positive integer n.2 + 4 + 8 + ... + 2^n = 2^(n+1) - 2

In Exercises 11–24, use mathematical induction to prove that each statement is true for every positive integer n.1 + 2 + 2^2 + ... + 2^(n-1) = 2^n - 1

In Exercises 11–24, use mathematical induction to prove that each statement is true for every positive integer n.3 + 7 + 11 + ... + (4n - 1) = n(2n + 1)

In Exercises 11–24, use mathematical induction to prove that each statement is true for every positive integer n.1 + 3 + 5 + ... + (2n - 1) = n^2

In Exercises 11–24, use mathematical induction to prove that each statement is true for every positive integer n.4 + 8 + 12 + ... + 4n = 2n(n + 1)