Chapter 9 Practice Quest

Simplify the expression.

Hint: Draw a number line to help you expand n-factorial.

Use Pascal's Triangle or the Binomial Theorem to expand (5x +y)⁴.

Hint: For grading purposes, write your answer as a simplified polynomial expression with x decreasing in power and y increasing in power. Remember that the first row of Pascal's triangle is n = 0.

Determine the 7th term in the expansion of (5x -2y)¹².

State the first five terms of the sequence defined recursively.

Note: For grading purposed, your answer should be entered as sequence of numbers: a₁, a₂, a₃, a₄, a₅

State the first five terms of the sequence defined explicitly.

Note: For grading purposed, your answer should be entered as sequence of numbers: a₁, a₂, a₃, a₄, a₅

What is the 9th term in the sequence?

Hint: a_n = a₁(r)^n-1

Given:

Determine the nth term of the arithmetic sequence.

Match the limit to the correct value, if it exists.

Express the series using sigma notation.

_{Note: Use k as the index variable.}

Find the sum of the first 25 terms of the sequence:

Find the sum of the first 8 terms of the series:

Match the sum to the correct value, if it exists.

Use the ratio test to determine the ratio of the series, then determine if the series is convergent or divergent.