Exam 9: Sequences, Series, and Probability

Find the probability of rolling a 5 on a 6-sided die.

Find the probability for the experiment of selecting a single card from a deck of 52 cards and have it be a spade.

Find the probability for the experiment of selecting a single card from a deck of 52 cards and have it be an even number.

Prove the statement using mathematical induction for all positive integers, n.+ + + ... + =

Find the term of the sequence = .

Expand using Pascal's Triangle.

Evaluate the finite series.

Evaluate the finite series.

Write the formula for the term of the geometric sequence with = 10 and r = - .

Find the probability of not occurring if

Prove the statement using mathematical induction for all positive integers, n.+ + + ... + = 1 -

Expand using the binomial theorem.

Expand using Pascal's Triangle.

Find the probability of tossing a coin 2 times and getting exactly 2 heads. Express the answer as a decimal.

Prove the statement using mathematical induction for all positive integers, n.+ + ... + =

Find the term of the sequence = .

Find the common ratio of the geometric sequence -3, 6, -12, 24, -48, ...

Find the first four terms of the sequence = -3n + 9, for n = 1, 2, 3, ... If the sequence is arithmetic, find the common difference d.

Evaluate the binomial coefficient .

The population of a city increased at the rate of 4% every year over an eight-year period. If the population was 4,000 in 2000, what was the population in 2005?