✏️ Self-Study Edition
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Sigma Notation
From Zero to Hero — 20 Essential Problems
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📌 Quick Formula Cheat Sheet
Sum of constants
\(\displaystyle\sum_{k=1}^{n} c = cn\)
Sum of first n integers
\(\displaystyle\sum_{k=1}^{n} k = \frac{n(n+1)}{2}\)
Sum of squares
\(\displaystyle\sum_{k=1}^{n} k^2 = \frac{n(n+1)(2n+1)}{6}\)
Sum of cubes
\(\displaystyle\sum_{k=1}^{n} k^3 = \left[\frac{n(n+1)}{2}\right]^2\)
Linearity
\(\displaystyle\sum_{k=1}^{n}(af_k + bg_k) = a\sum f_k + b\sum g_k\)
Telescoping
\(\displaystyle\sum_{k=1}^{n}(a_{k+1}-a_k) = a_{n+1} - a_1\)