Recent questions tagged ch4

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

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

If a square matrix A is such that $AA^T=I=A^TA$ then $|A|$ is equal to

asked Apr 25, 2014 by sreemathi.v

1 answer

If $A$ is square matrix of order $n\times n$ then adj(adj(A)) is equal to

asked Apr 25, 2014 by sreemathi.v

1 answer

The number of non trivial solutions of the system $x-y+z=0,x+2y-z=0,2x+y+3z=0$ is

asked Apr 25, 2014 by sreemathi.v

1 answer

If $ax^3+bx^2+cx+d=\begin{vmatrix}x^2&(x-1)^2&(x-2)\\(x-)^2&(x-2)^2&(x-3)^2\\(x-2)^2&(x-3)^2&(x-4)^2\end{vmatrix}$ then

asked Apr 25, 2014 by sreemathi.v

1 answer

The values of $\lambda$ and $\mu$ for which the equations $x+y+z=3,x+3y+2z=6,x+\lambda y+3z=\mu$ have

asked Apr 25, 2014 by sreemathi.v

1 answer

If $1+\sin x+\cos x\neq 0$ the value of $x$ for which $\begin{vmatrix}1&\sin x&\cos x\\\sin x&1&\cos x\\\cos x&\sin x&1\end{vmatrix}=0$ is

asked Apr 25, 2014 by sreemathi.v

1 answer

If $f(x)=\begin{vmatrix}\cos x&1&0\\1&2\cos x&1\\0&1&2\cos x\end{vmatrix}$ then $\int\limits_0^{\large\frac{\pi}{2}}2f(x)dx$ is equal to

asked Apr 25, 2014 by sreemathi.v

1 answer

If $A=\begin{vmatrix}a&b&c\\x&y&z\\p&q&r\end{vmatrix}$ and $B=\begin{vmatrix}q&-b&y\\-p&a&-x\\r&-c&z\end{vmatrix}$ then

asked Apr 24, 2014 by sreemathi.v

1 answer

If $A$ is a square matrix of order $n\times n$ then adj.(adj A) is equal to

asked Apr 24, 2014 by sreemathi.v

1 answer

If $D_r=\begin{vmatrix}2^{r-1}&2.3^{r-1}&4.5^{r-1}\\\alpha&\beta&\gamma\\2^n-1&3^n-1&5^n-1\end{vmatrix}$ then the value of $\sum\limits_{r=1}^n D_r$ is

asked Apr 24, 2014 by sreemathi.v

1 answer

If the system of linear equations :$x+2ay+az=0,x+3by+bz=0,x+4cy+cz=0$ has a zero solutions then $a,b,c$

asked Apr 24, 2014 by sreemathi.v

1 answer