Partial Sums Quizzes, Questions & Answers

Top Trending Partial Sums Quizzes

Alternating Series & Error Bounds Through Partial Sums

Partial sums provide a powerful way to understand how a series behaves term by term. By examining how Sₙ evolves, we can uncover the structure of the underlying sequence, determine whether a series converges or diverges, and...

Questions: 15 | Attempts: 12 | Last updated: Feb 6, 2026

Sample Question 1
Consider the infinite series defined by the summation of aₙ where aₙ = 2n - 1. What is the value of the third partial sum, S_3?

5

9

12

15

Sample Question 2
Which of the following formulas correctly represents the n-th partial sum, Sₙ, of a geometric series with first term a and common ratio r (where r is not equal to 1)?

A(1 - rⁿ)/(1 - r)

A/(1 - r)

A(rⁿ - 1)/(1 - r)

Arⁿ⁻¹

Using Partial Sums to Approximate Infinite Series

Partial sums offer a powerful window into how a series behaves—revealing whether it converges, diverges, telescopes, or follows familiar formulas such as those for geometric or arithmetic sums. In this quiz, you'll...

Questions: 15 | Attempts: 18 | Last updated: Feb 6, 2026

Sample Question 1
The second partial sum of a series is 8 and the third partial sum is 12. What is the third term a₃?

2

4

12

20

Sample Question 2
Find the 6th partial sum of the series: 1 + 1/2 + 1/4 + 1/8 + ...

63/32

31/16

63/64

127/64

Recent Partial Sums Quizzes

Telescoping Series, p-Series, and Integral Test: Understanding Sₙ and Convergence

Understanding partial sums is fundamental to analyzing infinite series and determining whether they converge or diverge. In this quiz, you’ll explore how individual terms relate to their cumulative sums, work with geometric...

Questions: 15 | Attempts: 11 | Last updated: Feb 6, 2026

Sample Question
Consider the series defined by aₙ = 2 + (-1)ⁿ / 2. Calculate the third partial sum, S_3.

4.5

5.0

5.5

6.0

Partial Sums of Arithmetic & Geometric Series

Understanding partial sums is essential for analyzing how sequences and series behave, whether they converge, diverge, or approximate important values. This quiz explores arithmetic and geometric series, telescoping sums,...

Questions: 15 | Attempts: 16 | Last updated: Feb 6, 2026

Sample Question
What is the fourth partial sum of the arithmetic sequence: 2, 5, 8, 11, 14, ...?

26

30

38

40