## How many pattern of two underlines...

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we have number from 1 to 2014. If we underline the number that divide by 3 and 4, how many pattern of two underlines that next to each other as example?(1,2,3,4,5,6,7,8,9,10,...,2014).

## Sequence of integers...

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Let a(1)=916 , a(2)=935 , a(3)=713  , a(4)=845  , a(5)=274  , a(6)=914 ,a(7)=255 . Find formula a(n)= ? ,n=1,2,3,....

## solve the system of equations...

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solve the system of equations (10a+3b+4c+d+e=0,11b+2c+2d+3e+f=0,15c+4d+5e+4f+g=0,2a+b-3c+12d-3e+f+g=0,6a-5b+3c-d+17e+f=0,3a+2b-3c+4d+e-16f+2g=0,4a-6b+c+d+3e+19g=0)

## functional equation...

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If f(n)=a^n+b^n+c^n   and f(1)=1,f(2)=2,f(3)=3 ,n=1,2,3,.... Find f(5) ?

## Geometry (Problem of Plane)...

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Given the pencil of lines a(3x+4y-10)+b(3x-y-5)=0.Find pencil of lines is tangent to the circle x^2+y^2+2x-4y=0?

## Solve the equation...

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Solve the equation :x=(2012-x)^1/2(2013-x)^1/2+(2013-x)^1/2(2014-x)^1/2+(2012-x)^1/2(2014-x)^1/2

## Sequence of real numbers...

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Find a(n)of sequence3,9,18,54,63,...   (n=1,2,3,4,...) ,

## Cubic Equation...

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If a, b and c are the roots of the equation x^3-x^2-x-1=0.
Find S=(a^2014-b^2014)/(a-b)+(b^2014-c^2014)/(b-c)+(c^2014-a^2014)/(c-a)

## Number Theory (multiply)...

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Replace each letter in the following multiply by a digit from 0 to 9 in such a way that the multiply  is correct.

HUNSEN*3=STRONG

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Find

## Number Theory (prime numbers )...

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Find all prime numbers from 500 to 600.

## limit [definite sum]...

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Find $\lim_{n \to \infty}(\frac{1}{n+1}+\frac{1}{n+2}+\frac{1}{n+3}+\dots+\frac{1}{n+n})$

## Limit (asymptotic)...

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Find $\lim_{n\to\infty}{\frac{\sqrt[n]{n!}}{n}}$

## Probability [mean, variance of min of a pair]...

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In a pocket, we have $5$ balls number from $1$ to

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