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

Find 3 + 6 + 9 + ... + 300, the sum of the first 100 positive multiples of 3.

Evaluate each factorial expression. 18!/16!

Use the Binomial Theorem to expand each binomial and express the result in simplified form. (x − 1)⁵

Use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.

${\sum }_{i=1}^{16}(3i+2)$

Use the formula for the sum of the first n terms of a geometric sequence to solve Exercises 25–30. Find the sum of the first 12 terms of the geometric sequence: 2, 6, 18, 54, ...

Write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for a_n to find a₂₀, the 20th term of the sequence. 7,3,-1,-5,...

Use mathematical induction to prove that each statement is true for every positive integer n. 2 is a factor of n² - n.

Evaluate each expression.

$\frac{{}_7{C}_3}{{}_5{C}_4}-\frac{98!}{96!}$

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

In Exercises 23–28, evaluate each factorial expression. 20!/2!18!

Evaluate each factorial expression. (n+2)!/n!

Use mathematical induction to prove that each statement is true for every positive integer n. 6 is a factor of n(n + 1)(n + 2).

Write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for a_n to find a₂₀, the 20th term of the sequence. a₁ = 9, d=2

Use the Binomial Theorem to expand each binomial and express the result in simplified form. (3x − y)⁵

Evaluate each expression.

$\frac{{}_4{C}_2{\cdot }_6{C}_1}{{}_{18}{C}_3}$

Use the formula for the sum of the first n terms of a geometric sequence to solve Exercises 25–30. Find the sum of the first 11 terms of the geometric sequence: 3, - 6, 12, - 24, ...

In Exercises 23–28, evaluate each factorial expression. (2n+1)!/(2n)!

Use mathematical induction to prove that each statement is true for every positive integer n. ${\sum }_{i=1}^{n}5\cdot 6^i=6(6^n-1)$

Find each indicated sum. ${\sum }_{i=1}^{6}5i$

Write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for a_n to find a₂₀, the 20th term of the sequence. a₁=-20, d = -4

Use the formula for the sum of the first n terms of a geometric sequence to solve Exercises 25–30. Find the sum of the first 14 terms of the geometric sequence: - 3/2, 3, - 6, 12, ...

Use the Fundamental Counting Principle to solve Exercises 29–40. The model of the car you are thinking of buying is available in nine different colors and three different styles (hatchback, sedan, or sport). In how many ways can you order the car?

Use the Binomial Theorem to expand each binomial and express the result in simplified form. (2a + b)⁶

Use the Fundamental Counting Principle to solve Exercises 29–40. A popular brand of pen is available in three colors (red, green, or blue) and four writing tips (bold, medium, fine, or micro). How many different choices of pens do you have with this brand?

Write the first three terms in each binomial expansion, expressing the result in simplified form. (x+2)⁸

Find each indicated sum. ${\sum }_{i=1}^{4}2i^2$

Write a formula for the general term (the nth term) of each arithmetic sequence. Do not use a recursion formula. Then use the formula for a_n to find a₂₀, the 20th term of the sequence. a_n = a_n-1 +3, a₁ = 4

Use mathematical induction to prove that each statement is true for every positive integer n. n + 2 > n

Use the Fundamental Counting Principle to solve Exercises 29–40. An ice cream store sells two drinks (sodas or milk shakes) in four sizes (small, medium, large, or jumbo) and five flavors (vanilla, strawberry, chocolate, coffee, or pistachio). In how many ways can a customer order a drink?