Best Homework Help For Sequences and Series

Sequences:

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.

Series:

The summation of elements of the sequence is called series. A series could converge or diverge, depending upon the characteristic of the sequence.

Sequences And Series Sample Questions:

Question 1: Given the sequence. Write the value of 

Answer: 

Explanation: The subscript of the term , tells us the position of the element. 

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Question 2: Find the sum of .

Answer: 

Explanation: Rewrite the given sequence in standard form.

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Question 3: Write the first three terms of  

Answer: 

Explanation: Since the series starts from , let us plug the value as .

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Question 4: If, , and . Write an expression for .

Answer: 

Explanation: We know, for , And .

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Question 5: Write the sum of infinite geometric series 

Answer: 

Explanation: We have, , and

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Question 6: Find the sum 

Answer: The series diverges.

Explanation: The series has a common ratio .

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Question 7: Check if the partial sum of the series converges or diverges. Given .

Answer: Diverges.

Explanation: It is an infinite series. So, .

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Question 8: Find the partial sum of the series. 

Answer: 

Explanation: It is an infinite series. So, 

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Question 9: Given . Write an expression for .

Answer:

Explanation: Notice that the numerator is having a power of 5. And, denominators have a continuous power of 3.

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Question 10: Find 

Answer: 

Explanation: Get the first and last term of the series.

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