Exam 10: Sequences and Series

Find the coefficient, C, of the term in the binomial expansion. Binomial: (x - 3y)⁶ Term: Cx³y³

Find the sum of the finite geometric series .

Evaluate the binomial coefficient .

Write the first four terms of the sequence defined by the recursion formula. Assume the sequence begins at 1. A₁ = 2 a_n = a_n-1 + 6

Find the common difference d of the arithmetic sequence 172, 166, 160, 154, 148,....

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

Find the term a₅ of the sequence

Expand using the binomial theorem.

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

Expand (x - 2)⁵ using the binomial theorem.

Find the coefficient, C, of the term in the binomial expansion. Binomial: (x + 5)⁹ Term: Cx⁶

Find the coefficient, C, of the term in the binomial expansion. Binomial: (x + 3)⁹ Term: Cx⁶

Find the sum:

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

Evaluate the binomial coefficient .

Find the sum of the first 50 terms of the series 7 + 13 + 19 + 25 + ...

Write the first four terms of the following sequence. Assume that n starts at 1. Do not reduce fractions.

Find the sum. , where

Find the sum.

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