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# Class 11 Maths PMI Lecture 1

# Lecture - 1 Chapter 4 Principle of Mathematical Induction

Posted on by Ashish Kumar

The successful warrior is the average man, with laser-like focus. – Bruce Lee

Exercise 4.1 |

Introduction to Principle of mathematical induction, explanation using dominoes

Proof of Arithmetic Progression using PMI

a+(a+d)+(a+2d)+…+(a+(n-1)d) = \frac{n}{2} (2a+(n-1)d)

**Question 1. ** 1+3+3^2+…+3^{n-1} = \frac{(3^n-1)}{2}

**Question 2. ** 1^3+2^3+3^3+…+n^3= \left ( \frac{n(n+1)}{2} \right )^2

**Question 3. ** 1+\frac{1}{(1+2)}+\frac{1}{(1+2+3)}+…+\frac{1}{(1+2+3+…+n)}=\frac{2n}{(n+1)}

**Question 4. ** 1.2.3+2.3.4+…+n(n+1)(n+2)=\frac{n(n+1)(n+2)(n+3)}{4}

**Question 5. ** 1.3+2.3^2+3.3^3+…+n.3^n=\frac{(2n-1)3^{n+1}+3}{4}

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