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 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.

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