Special Series

Mediummathematics

The sum 1³ + 2³ + 3³ + ... + n³ equals

Select the correct option:

[n(n+1)/2]²

n²(n+1)²/4

n(n+1)(2n+1)/6

n⁴/4

🔒 Solution Hidden from View

Submit your answer to unlock the detailed step-by-step solution.

About This Question

Subject: mathematics
Chapter: sequence and series
Topic: special series
Difficulty: Medium
Year: 2025

Solution

Correct Answer:

[n(n+1)/2]²

Interesting Property: The sum of the cubes of the first $n$ natural numbers is exactly equal to the square of the sum of the first $n$ natural numbers.
Formula: $\sum_{k = 1}^{n} k^{3} = (\frac{n ( n + 1 )}{2})^{2}$ .
Application: Total $= \frac{n ^{2} ( n + 1 ) ^{2}}{4}$ .

This medium difficulty mathematics question is from the chapter sequence and series, covering the topic of special series. It appeared in the 2025 exam.

Looking for more practice? Explore all mathematics questions or browse sequence and series questions on RankGuru.

Special Series

Select the correct option:

Solution

🔒 Solution Hidden from View

More special series Practice Questions

Determine the exact value of the convergent infinite sum whose kth term is k/2^k, taken over all pos...

Evaluate the value of the finite sum 1^2 + 2^2 + 3^2 + ... + 10^2 using the standard formula for the...

The sum 1² + 2² + 3² + ... + n² equals

The sum 1 + 2 + 3 + ... + n equals

About This Question

Solution