9. Sequences, Series, & Induction

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+ar+ar2+⋯+ ar^12

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)+⋯+ (a+nd)

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

5Σi=1 (a_i^2+1)

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

5∑i=1 (2a_i+b_i)

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

5Σi=1 (a_i+3b_i)

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

5Σi=4 (a_i/b_i)^2

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

5Σi=4 (a_i/b_i)^3

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

5Σi=1 a_i^2+5Σi=1 b_i^2

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

5Σi=1 a_i^2−5Σi=3 b_i^2

In Exercises 81–85, use a calculator's factorial key to evaluate each expression. 200!/198!

In Exercises 81–85, use a calculator's factorial key to evaluate each expression. (300/20)!

In Exercises 81–85, use a calculator's factorial key to evaluate each expression. 20!/300

In Exercises 81–85, use a calculator's factorial key to evaluate each expression. 20!/(20−3)!

In Exercises 81–85, use a calculator's factorial key to evaluate each expression. 54!/(54−3)!3!

Write the first five terms of the sequence whose first term is 9 and whose general term is an= (an−1)/2 if a_n-1 is even, a_n=3a_n-1 + 5 if a_n-1 is odd for n≥2.