Tính tích:
\(A=\left(\frac{3}{429}-\frac{1}{1\times3}\right)\times\left(\frac{3}{429}-\frac{1}{3\times5}\right)\times...\times\left(\frac{3}{429}-\frac{1}{119\times121}\right)\times\left(\frac{1}{429}-\frac{2}{121\times123}\right)\)
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(3/429 - 1/1.3)(3/429 - 1/3.5) ... (3/429 - 1/121.123)
= (1/143 - 1/1.3)(1/143 - 1/3.5) ... (1/143 - 1/11.13) ... (1/143 - 1/121.123)
= (1/11.13 - 1/1.3)(1/11.13 - 1/3.5) ... (1/11.13 -1/11.13) ... (1/11.13 - 1/121.123)
= (1/11.13 - 1/1.3)(1/11.13 - 1/3.5) ... 0 ... (1/11.13 - 1/121.123)
= 0
=(1/143-1/1.3)...(1/143-1/121.123)
vì trong tích có thừa số (1/143-1/11.13)=0
nên cả tích =0
LÀM ƠN LIKE CHO MÌNH ĐI
\(A=\frac{1}{2}\left(1+\frac{1}{1\cdot3}\right)\left(1+\frac{1}{2\cdot4}\right)...\left(1+\frac{1}{2015\cdot2017}\right)\)\(A=\frac{1}{2}\left(\frac{1\cdot3+1}{1\cdot3}\right)\left(\frac{2\cdot4+1}{2\cdot4}\right)...\left(\frac{2015\cdot2017+1}{2015\cdot2017}\right)\)
\(A=\frac{1^2}{2}\cdot\frac{2^2}{1\cdot3}\cdot\frac{3^2}{2\cdot4}\cdot\cdot\cdot\frac{2016^2}{2015\cdot2017}\)
\(A=\frac{1^2\cdot2^2\cdot3^2\cdot\cdot\cdot2016^2}{2\cdot1\cdot3\cdot2\cdot4\cdot\cdot\cdot2015\cdot2017}\)
\(A=\frac{2016}{2017}\)
\(d=\left(1+\frac{1}{1.3}\right)\left(1+\frac{1}{2.4}\right)\left(1+\frac{1}{3.5}\right).........\left(1+\frac{1}{99.101}\right)\)
\(=\frac{4}{3}.\frac{9}{2.4}.............\frac{10000}{99.101}\)
\(=\frac{2.2}{3}.\frac{3.3}{2.4}.\frac{4.4}{3.5}............\frac{100.100}{99.101}\)
\(=\frac{2.3.4..........100}{2.3.4............99}.\frac{2.3.4...........100}{3.4...........101}\)
\(=100.\frac{2}{101}\)\(=\frac{200}{101}\)
\(C=\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times...\times\left(1-\frac{1}{1994}\right)\)
\(=\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times...\times\frac{1993}{1994}\)
\(=\frac{1\times2\times3\times...\times1993}{2\times3\times4\times...\times1994}\)
\(=\frac{1}{1994}\) (Giản ước còn lại như này)
1=3/3=4/4=5/5=...
=> 1+1/1*3=3/1*3=1/1
=> 1+1/2*4=4/2*4=1/2
=>...
Bieu thuc se con lai la 1*1/2*1/3*1/4*1/5
Vay A=1/120
(3/429 - 1/1.3)(3/429 - 1/3.5) ... (3/429 - 1/121.123)
= (1/143 - 1/1.3)(1/143 - 1/3.5) ... (1/143 - 1/11.13) ... (1/143 - 1/121.123)
= (1/11.13 - 1/1.3)(1/11.13 - 1/3.5) ... (1/11.13 -1/11.13) ... (1/11.13 - 1/121.123)
= (1/11.13 - 1/1.3)(1/11.13 - 1/3.5) ... 0 ... (1/11.13 - 1/121.123)
= 0