Find the sum of all coefficients after expanding the expression: A = (3 - 4x + x2)2016.(3 + 4x + x2)2017
Find the sum of all coefficients after expanding the expression:
\(A=\left(3-4x+x^2\right)^{2016}\times\left(3+4x+x^2\right)^{^{ }2017}\)
Find the minimum value of the expression \(\frac{2}{-4x^2+8x-5}\)
Let N be the langest number ò region that can be formed by drawing 2016 straight lines on a plane. Find the sum ò all digits of N.
Find the value of the following expression:
20172 - 20162 + 20152 - 20142 + ... + 10032 - 10022
20172 - 20162 + 20152 - 20142 + ... + 10032 - 10022
= (2017 - 2016)(2016 + 2017) + (2015 - 2014)(2014 + 2015) + ... + (1003 - 2002)(1002 + 1003)
= 2017 + 2016 + 2015 + 2014 + ... + 1003 + 1002
= (1002 + 2017).1016 : 2
= 3019.508
= 1533652
Find the units digit of the sum: 12017 + 22017 + 32017 + … 82017 + 92017?
= 1 + 2 + 3 +...+8 + 9^2017
= 45^2017
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8.Find the value of 1+2+3+4+5+...+2016+2017+2016+2015+...+3+2+1.
\(=2\left(1+2+...+2016\right)+2017\\ =2\cdot\dfrac{\left(2016+1\right)\left(2016-1+1\right)}{2}+2017\\ =2017\cdot2016+2017=2017^2=4068289\)
1) ABC is a triangle where M is the midpoint of segment BC.
MD and ME are two bisectors of triangles AMB and AMC respectively.
If AM= m; BC = a . Then DE = ???
2)\(\dfrac{1}{\left(x+29\right)^2}+\dfrac{1}{\left(x+30\right)^2}=\dfrac{5}{4}\)
What is the product of all real solutions to the equation above?
3) The sum of all possible natural numbers n such that
\(n^2+n+1589\) is a perfect square is.....
4) Given that x is a positive integer such that x and x+99 are perfect squares
The sum of integer x is ...
5)The operation @ on two numbers produces a number equal to their sum minus 2. The value of
(...((1@2)@3....@2017)
6) Given f(x)=\(\dfrac{x^2}{2x-2x^2-1}\)
=> \(f\left(\dfrac{1}{2016}\right)+f\left(\dfrac{2}{2016}\right)+f\left(\dfrac{3}{2016}\right)+...+f\left(\dfrac{2016}{2016}\right)\)
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The lengths of three sides of a triangle are all primes, and the perimeter of the triangle is 17. Find the sum of all possible value(s) of the second longest side.
the value of expression
a=1/2016+3/2016+5/2016+...+2015/2016
a =1/2016 + 3/2016+5/2016+...+2015/2016
=(1+2015)/ 2016 + (3+2013)/2016 +...+(1007 + 1009)/2016 (504 cap so)
=2016/2016+2016/2016+...+2016/2016(504 phan so)
=1+1+1+...+1(504 so)
=504