# 11.5.2. Series and Summation Notation

Given that and , use the properties of the summation notation to find the value of .

Show SolutionGiven that , find the value of using the properties of the summation notation .

Show SolutionThe sum of the monthly salaries of an employee at the end of a year is LE. Given that the sum increases by a rate of every year, use the summation notation to describe the sum of his salaries after 5 years of work, then determine this sum to the nearest two decimal places.

- ALE
- BLE
- CLE
- DLE

A man has sent a message to four of his friends, and each of them has sent the same message to another four friends and so on. Given that each person has received the message only once, determine how many people got the message in the sixth time.

Show SolutionAfter a gold mine was discovered, its production in the first year was kg, and the production after that every year was decreasing by of that of the year before. Use the summation notation to determine the amount of the produced gold during the first five years, and then find this amount and approximate the result to the nearest two decimal places.

- A
- B
- C
- D

A boy had e-mailed a message for four friends, then each friend e-mailed the same message to another four friends each of whom did the same, where each friend received the message once only. Determine the series using the summation notation, then find the total number of people who received the message by the sixth wave.

- A, 5 460
- B, 108
- C, 1 365
- D, 60

A child wants to build a pyramid of identical wooden cubes, where its top consists of one cube, the second row consists of two cubes, and the third row consists of three cubes and so on. Express the number of cubes used in building the pyramid using the summation notation, given that the pyramid consists of 5 rows, and find this number.

- A cubes
- B cubes
- C cubes
- D cubes

In the figure below of three equilateral triangles, the vertices of each smaller triangle bisect the sides of the larger one in which it is drawn, and the side length of the largest one is cm. Using the summation notation, find the series of their perimeters and the sum in centimetres.

- Acm
- Bcm
- Ccm
- Dcm