The sequence is an arrangement of numbers in a certain order. The numbers in this set of ordered arrangements are called elements. Example: . The position element of the sequence is denoted by the subscript.
The summation of elements of the sequence is called series. A series could converge or diverge, depending upon the characteristic of the sequence.
Question 1: Given the sequence. Write the value of
Explanation: The subscript of the term , tells us the position of the element.
Question 2: Find the sum of .
Explanation: Rewrite the given sequence in standard form.
Question 3: Write the first three terms of
Explanation: Since the series starts from , let us plug the value as .
Question 4: If, , and . Write an expression for .
Explanation: We know, for , And .
Question 5: Write the sum of infinite geometric series
Explanation: We have, , and
Question 6: Find the sum
Answer: The series diverges.
Explanation: The series has a common ratio .
Question 7: Check if the partial sum of the series converges or diverges. Given .
Explanation: It is an infinite series. So, .
Question 8: Find the partial sum of the series.
Explanation: It is an infinite series. So,
Question 9: Given . Write an expression for .
Explanation: Notice that the numerator is having a power of 5. And, denominators have a continuous power of 3.
Question 10: Find
Explanation: Get the first and last term of the series.