# NCERT Solutions for Class 11 Maths Chapter 4 Principle of Mathematical Induction

### NCERT Solutions for Class 11 Maths Chapter 4 Exercise 4.1

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Prove the following through principle of mathematical induction for all values of n, where n is a natural number.

1) 1+3++.+3n-1=$\frac { { (3 }^{ n }-1) }{ 2 }$

2: +2³+3³++n³ = ${ (\frac { n(n+1) }{ 2 } ) }^{ 2 }$

3: $1+\frac { 1 }{ 1+2 } +\frac { 1 }{ 1+2+3 } +......+\frac { 1 }{ 1+2+3+...+n } =\frac { 2n }{ n+1 }$

4: 1.2.3+2.3.4++n(n+1)(n+2)= $\frac { n(n+1)(n+2)(n+3) }{ 4 }$

5: 1.3+2.32+3.33++n.3n

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