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Recent questions tagged 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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