Question

Tìm x, biết:

a) x + 2x + 3x +....+2011x = 2012.2013

b) x-1  + x-2  = x-3  + x-4

  2011   2010  2009  2008

c) 1/1.3 +  1/3.5 + .... + 1/(2x-1)(2x+1) = 99/99

d) 1-3 + 3² - 3³ +...+ (-3)^x = 1-9¹⁰⁰⁶/4

 

Answer 1

a) (1+2+3+....+2011)x=2012.2013

<=>\(\frac{2011.2012}{2}\)x=2012.2013

<=>x=4026/2011

b)\(\frac{x-1}{2011}-1+\frac{x-2}{2010}-1=\frac{x-3}{2009}-1+\frac{x-4}{2008}-1\)

<=>\(\left(x-2012\right)\left(\frac{1}{2011}+\frac{1}{2010}-\frac{1}{2009}-\frac{1}{2008}\right)=0\)

<=>x=2012

c)dùng công thức \(\frac{2}{\left(2x-1\right)\left(2x+1\right)}=\frac{1}{2x-1}-\frac{1}{2x+1}\)

ta được 1-1/2x+1=2     giải ra được x

ok