Special Series

Easymathematics

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

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

n²(n+1)²/4

n(n+1)/2

n³/3

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About This Question

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

Solution

Correct Answer:

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

Formula Recognition: This represents the sum of the squares of the first $n$ natural numbers.
Standard Formula: $\sum_{k = 1}^{n} k^{2} = \frac{n ( n + 1 ) ( 2 n + 1 )}{6}$ .
Example Check ( $n = 3$ ):
- Sum $= 1 + 4 + 9 = 14$ .
- Formula estimate: $\frac{3 ( 4 ) ( 7 )}{6} = \frac{84}{6} = 14$ . Matches.

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

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