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