Special series include standard summation formulas: (1) Σn (from 1 to n) = n(n+1)/2; (2) Σn² = n(n+1)(2n+1)/6; (3) Σn³ = [n(n+1)/2]²; (4) Sum of first n odd numbers = n²; (5) Sum of first n even numbers = n(n+1). Example: Sum of 1+2+3+...+20 = 20(21)/2 = 210. Sum of 1²+2²+...+10² = 10(11)(21)/6 = 385. Sum of first 5 odd numbers = 5² = 25 (i.e., 1+3+5+7+9). Applications: Finding sums quickly without calculating individual terms. Exam tip: Memorize formulas 1-3. Derive formulas 4-5 using AP. Verify using small examples.