Math 1050 Chapter 9 Review: Factorials, Sequences, Geometric Series, and Binomial Theorem, Study notes of Mathematics

Download Math 1050 Chapter 9 Review: Factorials, Sequences, Geometric Series, and Binomial Theorem and more Study notes Mathematics in PDF only on Docsity! Math 1050 - Chapter 9 Review 1. Simplify the factorial expression (2n − 1)! · 5! (2n + 1)! · 3! . 2. Find a formula for the nth term of the arithmetic sequence with first term 6 and common difference −2. 3. Find a formula for an for the arithmetic sequence with 7 th term 8 and 13th term 6. 4. Find the partial sum 25 ∑ k=1 ( 3k + 1 4 ) . 5. Write an expression for the nth term of the geometric sequence with first term 5 and common ratio 0.2. Use this to find the fourth term of the sequence. 6. Find the sum of the finite geometric sequence 5 ∑ i=1 3(2)i−1. 7. Find the sum of the infinite geometric series ∞ ∑ n=1 3 ( 2 3 )n−1 . 8. Use mathematical induction to prove the formula for every positive integer n. 1 + 3 2 + 2 + 5 2 + · · · + 1 2 (n + 1) = n 4 (n + 3) 9. Use the Binomial Theorem to expand and simplify the expression (x + 2)5. 1