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bỏ tạm 38/25 ra 

=(9/10-11/15) +(13/21-15/28) +(197/4851-199/4950)

=1/6+1/12+1/20+...+1/49*50=2450

=3-2/2x3+4-3/3x4+5-4/4x5+....50-49/49x50

=1/2-1/3+1/3-...-1/50

1/2-1/50=12/25

=38/25+12/25=50/25

=2

kiểm tra lại đề giúp

cc

hello

Sai bét

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

\(\Rightarrow S=\frac{38}{25}+\frac{18}{20}-\frac{22}{30}+\cdot\cdot\cdot+\frac{394}{9702}-\frac{398}{9900}\)

\(\Rightarrow S=\frac{38}{25}+2\cdot\left(\frac{9}{20}-\frac{11}{30}+\cdot\cdot\cdot+\frac{197}{9702}-\frac{199}{9900}\right)\)

\(\Rightarrow S=\frac{38}{25}+2\cdot\left(\frac{9}{4\cdot5}-\frac{11}{5\cdot6}+\cdot\cdot\cdot+\frac{197}{98\cdot99}-\frac{199}{99\cdot100}\right)\)

\(\Rightarrow S=\frac{38}{25}+2\cdot\left(\frac{1}{4}+\frac{1}{5}-\frac{1}{5}-\frac{1}{6}+\cdot\cdot\cdot-\frac{1}{99}-\frac{1}{100}\right)\)

\(\Rightarrow S=\frac{38}{25}+2\cdot\left(\frac{1}{4}-\frac{1}{100}\right)\)

\(\Rightarrow S=\frac{38}{25}+2\cdot\left(\frac{25}{100}-\frac{1}{100}\right)\)

\(\Rightarrow S=\frac{38}{25}+2\cdot\frac{24}{100}\)

\(\Rightarrow S=\frac{38}{25}+2\cdot\frac{6}{25}\)

\(\Rightarrow S=\frac{38}{25}+\frac{12}{25}\)

\(\Rightarrow S=\frac{50}{25}=2\)