Exam 9: Sequences, Series, and Probability

Which relationship below can be shown to be true through mathematical induction?

Find the general, or , term of the sequence given = 7 and d = k.

Find the sum of the infinite geometric series 1 + + + + ... . Round the answer to 3 decimal places if necessary.

Expand using the binomial theorem.

Write an expression for the term of the sequence , , , , , ...

Prove the statement using mathematical induction for all positive integers, n. n(n + 1)(n + 2) is divisible by 3

Find the probability of either or occurring if P( ) = and and and are not mutually exclusive and

Expand using Pascal's Triangle.

Find the probability of tossing two die and rolling a sum that is less than 9.

A minor league baseball stadium has 160 seats in the front row, and each subsequent row has 15 more seats than the previous row. How many seats are in the stadium if there are 50 rows?

Simplify the ratio of factorials.

Use the formula for to evaluate .

Find the term of the sequence = .

Simplify the ratio of factorials .

Use the formula for to evaluate .

Use the formula for to evaluate .

Evaluate the binomial coefficient .

Write the first four terms of the sequence. Assume that n starts at 1.=

Find the term of the sequence -6, 0, 6, 12, ...

Find the coefficient, C, of the term in the binomial expansion.