9. Sequences, Series, & Induction

Find each indicated sum. ${\sum }_{i=5}^{9}11$

Find each indicated sum. ${\sum }_{i=0}^4\frac{(-1{)}^i}{i!}$

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

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

Express each sum using summation notation. Use $1$ as the lower limit of summation and $i$ for the index of summation. $2+2^2+2^3+\cdots +2^{11}$

Express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. 1+2+3+⋯+ 30

Express each sum using summation notation. Use 1 as the lower limit of summation and i for the index of summation. 1/2+2/3+3/4+⋯+ 14/(14+1)

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

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)

In Exercises 55–60, express each sum using summation notation. Use a lower limit of summation of your choice and k for the index of summation. 5+7+9+11+⋯+ 31

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

In Exercises 55–60, express each sum using summation notation. Use a lower limit of summation of your choice and k for the index of summation. $a+(a+d)+(a+2d)+\cdots +(a+nd)$

In Exercises 61–68, use the graphs of and to find each indicated sum.

${\sum }_{i=1}^5(a_i^2+1)$

In Exercises 61–68, use the graphs of and to find each indicated sum.

${\sum }_{i=1}^5(2a_i+b_i)$

In Exercises 61–68, use the graphs of and to find each indicated sum.

${\sum }_{i=1}^5(a_i+3b_i)$