Question

Tính :

C=\(\frac{\frac{2006}{3}+\frac{2006}{3}+...+\frac{2006}{2007}}{\frac{2006}{1}+\frac{2005}{2}+...+\frac{1}{2006}}\)

Answer 1

Ta có :

Tử số = \(\frac{2006}{2}+...+\frac{2006}{2007}\)

= 2006.(\(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2007}\))

MS= \(\frac{2006}{1}+\frac{2005}{2}+...+\frac{1}{2006}\)

= 2006+\(\frac{2007-2}{2}+\frac{2007-3}{3}+...+\frac{2007-2006}{2006}\)

=200+.(\(\frac{2007}{2}+\frac{2007}{3}+...+\frac{2007}{2006}\)) - ( 1+1+1+...+1 )(2006c/s1) 

= 2006 . (\(\frac{2007}{2}+...+\frac{2007}{2006}\))-2006

=\(\frac{2007}{2}+...+\frac{2007}{2006}\)

=2007.(\(\frac{1}{2}+...+\frac{1}{2006}\))

Khi đó : 

C= .... bạn tự đáp số 

và cuối cùng C = \(\frac{2006}{2007}\)