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\(A=\frac{\frac{4}{111}+\frac{4}{123}-\frac{4}{999}}{\frac{2}{111}+\frac{2}{123}+\frac{2}{999}}\)
\(=\frac{4.\left(\frac{1}{111}+\frac{1}{123}+\frac{1}{999}\right)}{2.\left(\frac{1}{111}+\frac{1}{123}+\frac{1}{999}\right)}\)
\(=\frac{4}{2}=2\)
\(=\frac{4.\left(\frac{1}{111}+\frac{1}{123}-\frac{1}{999}\right)}{2.\left(\frac{1}{111}+\frac{1}{123}-\frac{1}{999}\right)}=\frac{4}{2}=2\)
Sửa đề lại rồi đó hả bạn?!
\(=\frac{4}{111}:\frac{2}{111}+\frac{4}{123}:\frac{2}{123}-\frac{4}{999}:\frac{2}{999}\)
\(=\frac{4}{111}\times\frac{111}{2}+\frac{4}{123}\times\frac{123}{2}-\frac{4}{999}\times\frac{999}{2}\)
\(=2+2-2\)
\(=2\)
:))
\(Q=\left(\frac{1}{99}+\frac{12}{999}+\frac{123}{999}\right)\left(\frac{1}{2}-\frac{1}{3}-\frac{1}{6}\right)\text{ }\)
\(Q=\left(\frac{1}{99}+\frac{12}{999}+\frac{123}{999}\right)\left(\frac{3}{6}-\frac{2}{6}-\frac{1}{6}\right)\)
\(Q=\left(\frac{1}{99}+\frac{12}{999}+\frac{123}{999}\right).0\)
\(Q=0\)
Q=(1/99+12/999+123/999).(1/2-1/3-1/6) =(1/99+12/999+123/999).0 Q=0
\(\left(\frac{1}{99}+\frac{12}{999}+\frac{123}{999}\right)\left(\frac{1}{2}-\frac{1}{3}-\frac{1}{6}\right)\)
\(=\left(\frac{1}{99}+\frac{12}{999}+\frac{123}{999}\right).0\)
\(=0\)
\(\left(\frac{1}{99}+\frac{12}{999}+\frac{123}{9999}\right)\left(\frac{1}{2}-\frac{1}{3}-\frac{1}{6}\right)\)=\(\left(\frac{1}{99}+\frac{12}{999}+\frac{123}{9999}\right).0=0\)
Ta có: B= (1/99+12/999-123/9999).(1/2-1/3-1/6)
B= (1/99+12/999-123/9999).(3/6-2/6-1/6)
B= (1/99+12/999-123/9999).0
B= 0
B = (1/99+12/999-123/9999).(1/2-1/3-1/6)
B= (1/99+12/999+123/9999).0
B=0
tk mình nha !
=1/1*2+1/2*3+...+1/999*1000
=1/1-1/2+1/2-1/3+...+1/999-1/1000
=1-1/1000
So sánh A và B biết;
A = \(\frac{1}{2}.\frac{3}{4}.\frac{5}{6}...\frac{999}{1000}\)
B = \(\frac{2}{3}.\frac{3}{4}.\frac{4}{5}...\frac{998}{999}\)
1-1/2+1/3-1/4+......-1/1000
=(1+1/3+1/5+......+1/999)-(1/2+1/4+.......+1/1000)
=(1+1/2+1/3+1/4+.....+1/1000)-2(1/2+1/4+.......+1/1000)
=(1+1/2+1/3+.........+1/1000)-(1+1/2+.....+1/500)
=1/501 +1/502+1/503+.....+1/1000 ;
mat khác:
500-500/501-501/502-.....-999/1000
=(1-500/501)+(1-501/502)+.....+(1-999/1000)=1/501+1/502+....+1/1000
=>D=1
\(\frac{\frac{4}{111}+\frac{4}{123}+\frac{4}{999}}{\frac{2}{111}+\frac{2}{123}+\frac{2}{999}}=\frac{4.\left(\frac{1}{111}+\frac{1}{123}+\frac{1}{999}\right)}{2.\left(\frac{1}{111}+\frac{1}{123}+\frac{1}{999}\right)}=\frac{4}{2}=2\)
\(=\frac{2\left(\frac{2}{111}+\frac{2}{123}+\frac{2}{999}\right)}{\frac{2}{111}+\frac{2}{123}+\frac{2}{999}}\)
\(=2\)