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Questions >> CBSE XI >> Math >> Principle of Mathematical Induction

Prove the following by using the principle of mathematical induction for all $n \in N$ $a+ar+ar^2+...+ar^{n-1}=\large\frac{a(r^n-1)}{r-1}$

asked Apr 30, 2014 by thanvigandhi_1

1 answer

Prove the following by using the principle of mathematical induction for all $n \in N$ $\large\frac{1}{1.2.3}$ $+\large\frac{1}{2.3.4}$ $+\large\frac{1}{3.4.5}$ $+...+\large\frac{1}{n(n+1)(n+2)}$ $=\large\frac{n(n+3)}{4(n+1)(n+2)}$

asked Apr 30, 2014 by thanvigandhi_1

1 answer

Prove the following by using the principle of mathematical induction for all $n \in N$ $\large\frac{1}{2.5}$ $+\large\frac{1}{5.8}$ $+\large\frac{1}{8.11}$ $+...+\large\frac{1}{(3n-1)(3n+2)}$ $=\large\frac{1}{(6n+4)}$

asked Apr 29, 2014 by thanvigandhi_1

1 answer

Prove the following by using the principle of mathematical induction for all $n \in N$ $\large\frac{1}{2}$ $+ \large\frac{1}{4}$ $+\large\frac{1}{8}$ $+...+\large\frac{1}{2^n}$ $=1-\large\frac{1}{2^n}$

asked Apr 29, 2014 by thanvigandhi_1

1 answer

Prove the following by using the principle of mathematical induction for all $n \in N$ $1.2+2.2^2+3.2^2+...+n.2^n=(n-1)2^{n+1}+2$

asked Apr 29, 2014 by thanvigandhi_1

1 answer

Prove the following by using the principle of mathematical induction for all $n \in N$ $1.3+3.5+5.7+...+(2n-1)(2n+1)= \large\frac{n(4n^2+6n-1)}{3}$

asked Apr 29, 2014 by thanvigandhi_1

1 answer

Prove the following by using the principle of mathematical induction for all $n \in N$ $1.2+2.3+3.4+...+n.(n+1) \bigg[ \large\frac{n(n+1)(n+2)}{3} \bigg]$

asked Apr 29, 2014 by thanvigandhi_1

1 answer

Prove the following by using the principle of mathematical induction for all $n \in N$ $1.3+2.3^2+3.3^3+...+n.3^n=\large\frac{(2n-1)3^{n+1}+3}{4}$

asked Apr 29, 2014 by thanvigandhi_1

1 answer

Prove the following by using the principle of mathematical induction for all $n \in N$ $1.2.3 + 2.3.4+...+n(n+1)(n+2)= \large\frac{n(n+1)(n+2)(n+3)}{4}$

asked Apr 29, 2014 by thanvigandhi_1

1 answer

Prove the following by using the principle of mathematical induction for all $n \in N$ $1+ \large\frac{1}{(1+2)}$ $+ \large\frac{1}{(1+2+3)}$ $+...+ \large\frac{1}{(1+2+3...n)}$ $= \large\frac{2n}{(n+1)}$

asked Apr 29, 2014 by thanvigandhi_1

1 answer

Prove the following by using the principle of mathematical induction for all $n \in N$ : $1^3+2^3+3^3+...+n^3= \bigg( \large\frac{n(n+1)}{2} \bigg)^2$

asked Apr 29, 2014 by thanvigandhi_1

1 answer

Prove the following by using the principle of mathematical induction for all $n \in N$ : $1+3+3^2+...+3^{n-1}= \large\frac{(3^n-1)}{2}$

asked Apr 29, 2014 by thanvigandhi_1

1 answer

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