Question

RÚT GỌN : 

\(\frac{3.13-13.18}{15.40-80}\)

\(\frac{2929-101}{2.1919+404}\)

CHỨNG TỎ RẰNG :

\(\frac{1}{101}+\frac{1}{102}+........+\frac{1}{149}+\frac{1}{150}>\frac{1}{3}\)

TÍNH HỢP LÍ :

\(B=\frac{5}{13}+\frac{-5}{7}-\frac{20}{41}+\frac{8}{13}+\frac{-21}{41}\)

 

Answer 1

RÚT GỌN:

\(\frac{3.13-13.18}{15.40-80}=\frac{13.\left(3-18\right)}{15.40-40.2}=\frac{13.\left(-15\right)}{40\left(15-2\right)}=\frac{13.\left(-15\right)}{40.13}=-\frac{15}{40}=-\frac{3}{8}\)

CHỨNG MINH:

Ta thấy \(\frac{1}{101}>\frac{1}{150};\frac{1}{102}>\frac{1}{150};...;\frac{1}{149}>\frac{1}{150}\)

=>\(\frac{1}{101}+\frac{1}{102}+...+\frac{1}{150}>\frac{1}{150}.\left(150-101+1\right)=\frac{1}{150}.50=\frac{50}{150}=\frac{1}{3}\)(đpcm)

TÍNH HỢP LÝ:

B=\(\frac{5}{13}+\frac{-5}{7}-\frac{20}{41}+\frac{8}{13}+\frac{-21}{41}=\left(\frac{5}{13}+\frac{8}{13}\right)+\left(\frac{-21}{41}-\frac{20}{41}\right)+\frac{-5}{7}=1+\left(-1\right)+\frac{-5}{7}=0+\frac{-5}{7}=\frac{-5}{7}\)