Question

tính thuận tiện

A = 38/25 + 9/10 -11/15 +..+ 197/4851 -199/4950

Answer 1

\(A=\frac{38}{25}+\frac{9}{10}-\frac{11}{15}+...+\frac{197}{4851}-\frac{199}{4950}\)

\(\frac{1}{2}.A=\frac{19}{25}+\frac{9}{20}-\frac{11}{30}+...+\frac{197}{97.99}-\frac{199}{99.100}\)

\(\frac{1}{2}.A=\frac{19}{25}+\frac{9}{4.5}-\frac{11}{5.6}+...+\frac{197}{98.99}-\frac{199}{99.100}\)

\(\frac{1}{2}.A=\frac{19}{25}+\frac{1}{4}+\frac{1}{5}-\left(\frac{1}{5}+\frac{1}{6}\right)+...+\left(\frac{1}{89}+\frac{1}{99}\right)-\left(\frac{1}{99}+\frac{1}{100}\right)\)

\(\frac{1}{2}.A=\frac{19}{25}+\frac{1}{4}-\frac{1}{100}\)

\(\frac{1}{2}.A=\frac{76}{100}+\frac{25}{100}-\frac{1}{100}\)

\(\frac{1}{2}.A=1\)

\(A=1:\frac{1}{2}\)

\(A=2\)