9. Sequences, Series, & Induction

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

${\sum }_{i=4}^5(a_i/b_i{)}^2$

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

${\sum }_{i=4}^5(a_i/b_i{)}^3$

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

${\sum }_{i=1}^5{a}_i^2+{\sum }_{i=1}^5{b}_i^2$

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

${\sum }_{i=1}^5{a}_i^2-{\sum }_{i=3}^5{b}_i^2$

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

$\frac{200!}{198!}$

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.

$\frac{20!}{300}$

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.

$\frac{54!}{(54-3)!3!}$

Write the first five terms of the sequence whose first term is 9 and whose general term is

for n≥2.

Use mathematical induction to prove that each statement is true for every positive integer n. 2 + 4 + 8 + ... + 2ⁿ = 2ⁿ⁺¹ - 2

Use mathematical induction to prove that each statement is true for every positive integer n. 1 + 2 + 2² + ... + 2^n-1 = 2^{n - 1}

Use mathematical induction to prove that each statement is true for every positive integer n. 3 + 7 + 11 + ... + (4n - 1) = n(2n + 1)

Use mathematical induction to prove that each statement is true for every positive integer n. 1 + 3 + 5 + ... + (2n - 1) = n²

Use mathematical induction to prove that each statement is true for every positive integer n. 4 + 8 + 12 + ... + 4n = 2n(n + 1)