Question

Answer 1

a: \(\frac{45\times16-17}{45\times15+28}\)

\(=\frac{45\times15+45-17}{45\times15+28}\)

\(=\frac{45\times15+28}{45\times15+28}=1\)

b:

Số số hạng trong dãy 1;4;...;55 là:

(55-1):3+1=54:3+1=19(số)

Tổng của dãy số 1;4;...;55 là:

\(\left(55+1\right)\times\frac{19}{2}=56\times\frac{19}{2}=28\times19=532\)

\(\frac{0,18\times1230+0,9\times4567\times2+3\times5310\times0,6}{1+4+7+\cdots+55-414}\)

\(=\frac{1,8\times123+1,8\times4567+1,8\times5310}{532-414}\)

\(=\frac{1,8\times\left(123+4567+5310\right)}{118}=\frac{1,8\times10000}{118}=\frac{18000}{118}=\frac{9000}{59}\)

c: \(A=\frac{2000\times2001-1000}{2000\times2000+1000}\)

\(=\frac{2000\times2000+2000-1000}{2000\times2000+1000}=\frac{2000\times2000+1000}{2000\times2000+1000}\)

=1

d: \(B=\frac{1}{1\times3}+\frac{1}{3\times5}+\cdots+\frac{1}{99\times101}\)

\(=\frac12\times\left(\frac{2}{1\times3}+\frac{2}{3\times5}+\cdots+\frac{2}{99\times101}\right)\)

\(=\frac12\times\left(1-\frac13+\frac13-\frac15+\cdots+\frac{1}{99}-\frac{1}{101}\right)\)

\(=\frac12\times\left(1-\frac{1}{101}\right)=\frac12\times\frac{100}{101}=\frac{50}{101}\)