Exam 9: Sequences, Series, and Probability

Prove the statement using mathematical induction for all positive integers, n.8 + 13 + 18 + ... + (5n + 3) = n(5n + 11)/2

Find the sum of the infinite geometric series .

Prove the statement using mathematical induction for all positive integers, n.+ + + ... + = ( - 1)/8

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

Find the probability of either or occurring if and are mutually exclusive and, and

Write the formula for the n^th term of the geometric sequence with = 7 and r = -10.

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

Evaluate the binomial coefficient .

Find the sum of the finite geometric series 5 + 10 + 20 + 40 + ... + 160.

If a state lottery picks from 59 numbers and 4 numbers are selected, how many possible 4-number combinations are there?

Evaluate the finite series.

Find the term of the geometric sequence , - , , - , ...

Find the sum of the finite geometric series . Round the answer to 3 decimal places if necessary.

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

Use the formula for to evaluate .

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

At the time she was hired, Nema's salary was $55,000 per year. If she is given an annual salary increase of 4% per year, what will her salary be after 5 years?

Evaluate the binomial coefficient .

Find the term of the sequence 8, 13, 18, 23, 28, ...

Find the probability of tossing a coin 7 times and getting exactly one head.