What is the value of 1³ + 2³ + 3³ + ... + n³ if 1 + 2 + ... + n = 15?
- 125
- 150
- 225
- 250
Explanation
1 + 2 + 3 + ... + n = 15
This is an arithmetic series. Use the formula:
n(n + 1)/2 = 15
→ Multiply both sides by 2:
n(n + 1) = 30
Try n = 5:
5(6) = 30
So, n = 5
Now calculate:
1³ + 2³ + 3³ + ... + n³
Use formula:
[n(n + 1)/2]² = [5×6/2]² = (15)² = 225
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