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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

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