Recent questions tagged sec3

Prove the rule of exponents $(ab)^n=a^nb^n$ by using principle of mathematical induction for every natural number.

asked May 5, 2014 by thanvigandhi_1

1 answer

Prove that \[\] $ 1^2+2^2+...+n^2 > \large\frac{n^3}{3}$$, n \in N$

asked May 5, 2014 by thanvigandhi_1

1 answer

Prove that \[\] $2.7^n+3.5^n-5$ is divisible by 24, for all $n \in N$.

asked May 3, 2014 by thanvigandhi_1

1 answer

Prove that $ (1+x)^n \geq (1+nx)$, for all natural number $n$, where $x > -1$.

asked May 3, 2014 by thanvigandhi_1

1 answer

For every positive integer $n$, prove that $7^n-3^n$ is divisible by 4.

asked May 3, 2014 by thanvigandhi_1

1 answer

For all $ n \geq 1$, prove that \[\] $ \large\frac{1}{1.2}$$+\large\frac{1}{2.3}$$+\large\frac{1}{3.4}$$+...+\large\frac{1}{n(n+1)}$$=\large\frac{n}{(n+1)}$.

asked May 2, 2014 by thanvigandhi_1

1 answer

Prove that $2^n > n$ for all positive integers $n$.

asked May 2, 2014 by thanvigandhi_1

1 answer

For all $n \geq 1$, prove that \[\] $ 1^2+2^2+3^2+4^4+...+n^2=\large\frac{n(n+1)(2n+1)}{6}$.

asked May 2, 2014 by thanvigandhi_1

1 answer

Prove the following by using the principle of mathematical induction for all $n \in N$ \[\] $ (2n+7) < (n+3)^2$

asked May 1, 2014 by thanvigandhi_1

1 answer

Prove the following by using the principle of mathematical induction for all $n \in N$ \[\] $ 41^n-14^n$ is a multiple of 27.

asked May 1, 2014 by thanvigandhi_1

1 answer

Prove the following by using the principle of mathematical induction for all $n \in N$ \[\] $ 3^{2n+2}-8n-9$ is divisible by 8.

asked May 1, 2014 by thanvigandhi_1

1 answer

Prove the following by using the principle of mathematical induction for all $n \in N$ \[\] $ x^{2n}-y^{2n}$ is divisible by $x+y$.

asked May 1, 2014 by thanvigandhi_1

1 answer

Prove the following by using the principle of mathematical induction for all $n \in N$ \[\] $ 10^{2n-1}+1$ is divisible by 11.

asked May 1, 2014 by thanvigandhi_1

1 answer

Prove the following by using the principle of mathematical induction for all n ∈ N: \[\] $ n(n+1)(n+5) $ is a multiple of 3.

asked May 1, 2014 by thanvigandhi_1

1 answer

Prove the following by using the principle of mathematical induction for all n ∈ N: \[\] $1+2+3+...+n<\large\frac{1}{8}$$(2n+1)^2$

asked May 1, 2014 by thanvigandhi_1

1 answer

Prove the following by using the principle of mathematical induction for all $n \in N$ \[\] $ \large\frac{1}{3.5}$$+\large\frac{1}{5.7}$$+\large\frac{1}{7.9}$$+...+\large\frac{1}{(2n+1)(2n+3)}$$=\large\frac{n}{3(2n+3)}$

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}{1.4}$$+\large\frac{1}{4.7}$$+\large\frac{1}{7.10}$$+...+\large\frac{1}{(3n-2)(3n+1)}$$=\large\frac{n}{(3n+1)}$

asked Apr 30, 2014 by thanvigandhi_1

1 answer

Prove the following by using the principle of mathematical induction for all $n \in N$ \[\] $ 1^2+3^2+5^2+...+(2n-1)^2=\large\frac{n(2n-1)(2n+1)}{3}$

asked Apr 30, 2014 by thanvigandhi_1

1 answer

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

asked Apr 30, 2014 by thanvigandhi_1

1 answer

Prove the following by using the principle of mathematical induction for all $n \in N$ \[\] $ \bigg( 1+ \large\frac{3}{1} \bigg)$$\bigg( 1+ \large\frac{5}{4} \bigg)$$\bigg( 1+ \large\frac{7}{9} \bigg)$$...\bigg( 1+ \large\frac{(2n+1)}{n^2} \bigg)$$=(n+1)^2$

asked Apr 30, 2014 by thanvigandhi_1

1 answer

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

asked Apr 30, 2014 by thanvigandhi_1

1 answer