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Sums and induction
Closed forms for sums, and how induction proves them.
Σ k = n(n+1)/2 is the formula Gauss found at school; Σ k² and Σ k³ have closed forms too. Induction proves them: check n = 1, then show that if the formula holds for n it holds for n + 1.
ឧទាហរណ៍ដែលបានធ្វើ: sum of k for k = 1 to n
ជំហានដោយជំហាន
- \sum_{k=1}^{n} k
Write the sum out.
- 1 + 2 + 3 + 4 + \cdots
The first few terms.
- = \frac{n \left(n + 1\right)}{2}
Closed form (a standard summation formula, provable by induction).
បង្ហាញចម្លើយ
\frac{n \left(n + 1\right)}{2}