tính thuận tiện
A = 38/25 + 9/10 -11/15 +..+ 197/4851 -199/4950
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HL
2
15 tháng 9 2021
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
DT
0
NT
2
NG
1
DD
0
5 tháng 9 2019
\(S=\frac{38}{25}+\frac{9}{10}-\frac{11}{15}+\cdot\cdot\cdot+\frac{197}{4851}-\frac{199}{4950}\)
\(\Rightarrow S=\frac{38}{25}+\frac{18}{20}-\frac{22}{30}+\cdot\cdot\cdot+\frac{394}{9702}-\frac{398}{9900}\)
\(\Rightarrow S=\frac{38}{25}+2\cdot\left(\frac{9}{20}-\frac{11}{30}+\cdot\cdot\cdot+\frac{197}{9702}-\frac{199}{9900}\right)\)
\(\Rightarrow S=\frac{38}{25}+2\cdot\left(\frac{9}{4\cdot5}-\frac{11}{5\cdot6}+\cdot\cdot\cdot+\frac{197}{98\cdot99}-\frac{199}{99\cdot100}\right)\)
\(\Rightarrow S=\frac{38}{25}+2\cdot\left(\frac{1}{4}+\frac{1}{5}-\frac{1}{5}-\frac{1}{6}+\cdot\cdot\cdot-\frac{1}{99}-\frac{1}{100}\right)\)
\(\Rightarrow S=\frac{38}{25}+2\cdot\left(\frac{1}{4}-\frac{1}{100}\right)\)
\(\Rightarrow S=\frac{38}{25}+2\cdot\left(\frac{25}{100}-\frac{1}{100}\right)\)
\(\Rightarrow S=\frac{38}{25}+2\cdot\frac{24}{100}\)
\(\Rightarrow S=\frac{38}{25}+2\cdot\frac{6}{25}\)
\(\Rightarrow S=\frac{38}{25}+\frac{12}{25}\)
\(\Rightarrow S=\frac{50}{25}=2\)
\(A=\frac{38}{25}+\frac{9}{10}-\frac{11}{15}+...+\frac{197}{4851}-\frac{199}{4950}\)
\(\frac{1}{2}.A=\frac{19}{25}+\frac{9}{20}-\frac{11}{30}+...+\frac{197}{97.99}-\frac{199}{99.100}\)
\(\frac{1}{2}.A=\frac{19}{25}+\frac{9}{4.5}-\frac{11}{5.6}+...+\frac{197}{98.99}-\frac{199}{99.100}\)
\(\frac{1}{2}.A=\frac{19}{25}+\frac{1}{4}+\frac{1}{5}-\left(\frac{1}{5}+\frac{1}{6}\right)+...+\left(\frac{1}{89}+\frac{1}{99}\right)-\left(\frac{1}{99}+\frac{1}{100}\right)\)
\(\frac{1}{2}.A=\frac{19}{25}+\frac{1}{4}-\frac{1}{100}\)
\(\frac{1}{2}.A=\frac{76}{100}+\frac{25}{100}-\frac{1}{100}\)
\(\frac{1}{2}.A=1\)
\(A=1:\frac{1}{2}\)
\(A=2\)