OLD 9. Sequences, Induction, and Probability

In Exercises 43–54, express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. 1+3+5+⋯+ (2n−1)

Find each indicated sum. ${\sum }_{i=1}^{4}2i^2$

Write the first four terms of each sequence whose general term is given. a_n = 7n - 4

Express each sum using summation notation. Use $1$ as the lower limit of summation and $i$ for the index of summation. $4+4^2/2+4^3/3+\cdots +4^n/n$

Use a calculator's factorial key to evaluate each expression. 20!/(20−3)!

In Exercises 8–9, find each indicated sum. This is a summation, refer to the textbook.

Evaluate $\frac{40!}{4!38!}$

Evaluate each factorial expression. (n+2)!/n!

Express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. $1^2+2^2+3^2+\cdots +{15}^2$

In Exercises 81–85, use a calculator's factorial key to evaluate each expression.

$\frac{20!}{300}$

Find each indicated sum. ${\sum }_{k=1}^{5}k(k+4)$

Express each sum using summation notation. Use a lower limit of summation of your choice and k for the index of summation. a+ar+ar²+⋯+ ar¹²

Find each indicated sum. ${\sum }_{i=1}^5\frac{i!}{(i-1)!}$