Business Contact: mathgotserved@ Epic Collection of Mathematical Induction : Prove 1) 1+2+3+...+n=n(n+1)/2 ----------------------------- 2) 2+2^2+2^3+...+2^n=2(2^n-1) -------------------- 3) 1+5+9+...+(4n-3)=n(2n-1)--------------------------- 4) 1/(1X2)+1/(2X3)+...+1/(n(n+1))=n/(n+1), 5) n^3+2n is divisible by 3,---------------------------- 6) n less 2n---------------------------------------------------- 7) 1+3+5+7+...+(2n-1)=n^2 for all n in N,----- 8) sum Σ k=1 to n k^2= 1/6n(n+1)(2n+1)---- 9) 9^n-2^n id divisible by 7,---------------------------- 10) 1+5+9+13+..+(4n-3)=½n(4n-2)---------------- 11) n Σ k =n(n+1)/2 sum of k n plus one over two--- 12) 1^3+2^3+3^3+..+n^3= (n(n+1)/2)^2 n^2(n+1)^2/4,----- 13) 10^1+10^2+10^3+...+10^n=10/9(10^n-1),---------------- 14) d/dx (x^-1)=(-1)^nn!/x^(n-1)----------------------- 15) 2^n greater or equal 1+n,------------------------ 16) 3^n less than (n+1)!,-------------------------------- 17) 8^n-1 is divisible by 7,----------------------------- 18) 10^n-3^n is divisible by 7------------------------- 19) 5^n-2^n is divisible by 3-------------------------- Math Tutorials Links Website Algebra Foundations Converting /Translating Verbal to Expressions Equations Order of Operations: Adding and Subtracting Integers Rationals: Multiplying and Dividing Rationals Integers The Distributive Property how to Equations Solve One Step Equations Solve Multi step equations solving how to Absolute Value Equations how to solve Mixture Problem how to solve Combined Work Word Problems Literal Equations How to Solve formulas Inequalities Graphing single variable inequalities Solve One Step Inequalities how to Solve two step inequalities Solving Multi Step Inequalities Solve Proportions solving Graphing how to Graph Linear Functions How to Graph Linear Inequalities Graph Absolute Value Equations Solve Systems of Equations by Graphing Systems of Equations by elimination Systems of Equations by substitution Systems of Linear Inequatlities The quotient property of exponents Domain and Range Precalculus Entire Collection Vectors Induction Discrete Math Proofs Matrices Unit Circle Identities Conic Sections Laws of Sines Cosines Ap Calculus Collection Ap calculus Limits Ap Calculus Derivatives Ap calculus Implicit Differentiation Optimization Extrema Maximum Minimum Solids of Revolution Definite Integral Integration Integration by Parts Related Rates Tabular Integration