special series

Question

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

RankGuru · Accepted Answer

1. **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.
2. **Formula**: $\sum_{k=1}^{n} k^3 = \left( \frac{n(n+1)}{2} \right)^2$.
3. **Application**: Total $= \frac{n^2(n+1)^2}{4}$.

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

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