Tính tổng :\(\frac{1}{5}+\frac{1}{20}+\frac{1}{44}+\frac{1}{77}+\frac{1}{119}+\frac{1}{170}+\frac{1}{230}+\frac{1}{299}\)

\(A=\frac{1}{5}+\frac{1}{20}+\frac{1}{44}+\frac{1}{77}+...+\frac{1}{299}+\frac{1}{377}\)

Tính A.

Tính giá trị biểu thức:

a) \(M=\frac{3}{299}.\left(2+\frac{1}{433}\right)-\frac{1}{229}.\frac{432}{433}-\frac{4}{229.433}\)

b) \(N=3.\frac{1}{117}.\frac{1}{119}-\frac{4}{117}.5\frac{118}{119}-\frac{5}{117.119}+\frac{8}{39}\)

\(\frac{1}{1\cdot300}+\frac{1}{2\cdot301}+\frac{1}{3\cdot302}+...+\frac{1}{299\cdot400}\)chứng minh rằng \(\frac{1}{299}\left(\left(1+\frac{1}{2}+...+\frac{1}{101}\right)-\left(\frac{1}{300}+\frac{1}{301}+...+\frac{1}{400}\right)\right)\)=\(\frac{1}{1\cdot300}+\frac{1}{2\cdot301}+\frac{1}{3\cdot302}+...+\frac{1}{299\cdot400}\)

\(Tính:A＝3\frac{1}{117}\times\frac{1}{119}-\frac{4}{117}\times5\frac{118}{119}-\frac{5}{117\times119}＋\frac{8}{39}\)

Tính hợp lí

a,

\(A=\left(-\frac{5}{11}+\frac{7}{22}-\frac{4}{33}-\frac{5}{44}\right).\left(\frac{837}{22}-\frac{865}{22}\right)\)

b, \(B=1-\frac{1}{1+\frac{2}{3-\frac{4}{5-7}}}\)

c, \(C=-\frac{1}{10}-\frac{1}{100}-\frac{1}{1000}-\frac{1}{10000}-\frac{1}{100000}\)

Tính:

a/\(\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2017}}{\frac{2016}{1}+\frac{2015}{2}+...+\frac{1}{2016}}\)

b/\(\frac{2\cdot2306}{1+\frac{1}{1+2}+\frac{1}{1+2+3}+...+\frac{1}{1+2+3+...+230}}\)c/\(\left(\frac{1}{4\cdot9}+\frac{1}{9\cdot14}+...+\frac{1}{44\cdot49}\right)\left(\frac{1-3-5-...-49}{89}\right)\)

a) A = \(3\frac{1}{117}.4\frac{1}{119}-1\frac{116}{117}.5\frac{118}{119}-\frac{5}{119}\)

b) B = \(4\frac{1}{115}.1\frac{1}{225}-5\frac{114}{115}.1\frac{224}{225}-\frac{10}{225}\)

Tính  A = \(3.\frac{1}{117}.\frac{1}{119}-\frac{4}{117}.5.\frac{118}{119}-\frac{5}{117}.\frac{1}{119}+\frac{8}{39}\)