Sum of Number Series (Basic Formulas)

Sum of Number Series (Basic Formulas)

A high-yield practice drill on standard arithmetic series summation formulas for Kerala PSC examinations (LDC, LGS, CPO, Fireman, Secretariat Assistant). Master key formulas: sum of first $$n$$ natural numbers ($$\frac{n(n+1)}{2}$$), first $$n$$ odd numbers ($$n^2$$), first $$n$$ even numbers ($$n(n+1)$$), sum of squares ($$\frac{n(n+1)(2n+1)}{6}$$), and sum of cubes ($$[\frac{n(n+1)}{2}]^2$$). Study Scope Sum of Natural Numbers: Direct calculation up to $$n=10, 20, 50, 100$$ ($$5050$$) Sum of Intermediate Ranges: Finding sums from $$11$$ to $$20$$ using difference of sums Sum of Odd Numbers: $$n^2$$ rule for first $$n$$ odd integers and odd numbers up to $$N$$ Sum of Even Numbers: $$n(n+1)$$ formula for first $$n$$ even numbers Sum of Squares & Cubes: Standard formula applications and connection between $$\sum n^3$$ and $$(\sum n)^2$$ Tested Competencies Select and apply the exact series summation formula without manual addition Calculate intermediate range series sums ($$\text{Sum}(b) - \text{Sum}(a-1)$$) Solve repeated Kerala PSC examination arithmetic questions quickly and error-free Cover: Portrait of Carl Friedrich Gauss by Christian Albrecht Jensen (Public domain). Source: Wikimedia Commons. Changes: Cropped to 16:9 aspect ratio and resized to 1200x675.