(1/2 - 1) (1/3 - 1) ... (1/2002 - 1) ( 1/2003) = ?
3/4.8/9.15/16 ..... 9999/10000 = ?
1) Tính
A= 3/4.8/9.15/16...9999/10000
B= (1-1/4).(1-1/9)...(1-1/1000)
\(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}....\frac{9999}{10000}\)
\(=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}.....\frac{99.101}{100.100}\)
\(=\frac{1.2.3....99}{2.3.4....100}.\frac{3.4.5....101}{2.3.4...100}\)
\(=\frac{1}{100}.\frac{101}{2}=\frac{101}{200}\)
\(B=\left(1-\frac{1}{4}\right).\left(1-\frac{1}{9}\right).....\left(1-\frac{1}{10000}\right)\)
\(=\frac{3}{4}.\frac{8}{9}....\frac{9999}{10000}=\frac{101}{200}\)
Tính các tích sau:
A= 3/4.8/9.15/16...9999/10000
B=(1-1/4).(1-1/9)...(1-1/10000).
C=(1+1/1.3)(1+1/2.4)(1+1/3.15)....(1+1/99.100).
A = \(\frac{3}{4}\cdot\frac{8}{9}\cdot\frac{15}{16}\cdot\cdot\cdot\cdot\frac{9999}{10000}=\frac{1\cdot3}{2.2}\cdot\frac{2\cdot4}{3\cdot3}\cdot\frac{3.5}{4.4}\cdot\cdot\cdot\cdot\frac{99\cdot101}{100\cdot100}=\frac{1}{2}\cdot\frac{101}{100}=\frac{101}{200}\)
B = ( 1- 1/4 )( 1-1/9) ...( 1-1/10000 ) = 3/4 . 8/9 .....9999/100000 ( tương tự A )
Tính nhanh:
1, A= 3/4.8/9.15/16......9999/10000
2, B = (1-1/2).(1-1/8)....(1-1/n+1)
giúp mk nha. đang cần gấp gấp lắm
thank you các bạn nhìu...
Thực hiện phép tính:
A=3/4.8/9.15/16...9999/10000
B=(1-1/3)(1-1/6)(1-1/10)(1-1/15)...(1-1/780)
Giúp mk với mk đang cần gấp
\(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.....\frac{9999}{10000}\)
\(A=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}.....\frac{99.101}{100.100}\)
\(A=\frac{\left(1.2.3.....99\right).\left(3.4.5.....101\right)}{\left(2.3.4.....100\right).\left(2.3.4.....100\right)}\)
\(A=\frac{1.101}{2.100}=\frac{101}{200}\)
\(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}......\frac{9999}{10000}\)
\(A=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}.....\frac{99.101}{100.100}\)
\(A=\frac{1.2.3.4.....99}{2.3.4.5.....100}.\frac{3.4.5.6.....101}{2.3.4.5.....100}\)
\(A=\frac{1}{100}.\frac{101}{2}\)
\(A=\frac{101}{200}\)
\(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}...\frac{9999}{10000}\)
\(A=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}...\frac{99.101}{100.100}\)
\(A=\frac{1.2...99}{2.3...100}.\frac{3.5...101}{2.3...100}\)
\(A=\frac{1}{100}.\frac{101}{2}\)
\(=\frac{101}{200}\)
\(B=\left(1-\frac{1}{3}\right)\left(1-\frac{1}{6}\right)\left(1-\frac{1}{10}\right)\left(1-\frac{1}{15}\right)...\left(1-\frac{1}{780}\right)\)
\(B=\frac{2}{3}.\frac{5}{6}.\frac{9}{10}.\frac{14}{15}...\frac{779}{780}\)
\(B=\frac{4}{6}.\frac{10}{12}.\frac{18}{20}....\frac{1558}{1560}\)
\(B=\frac{1.4}{2.3}.\frac{2.5}{3.4}.\frac{3.6}{4.5}...\frac{38.41}{39.40}\)
\(B=\frac{1.2.3...38}{2.3...39}.\frac{4.5...41}{3.4...40}\)
\(B=\frac{1}{39}.\frac{41}{3}\)
\(B=\frac{41}{117}\)
a, Tính tổng: 5/6+5/12+5/20+.......+5/132
b, Tìm x: 1/2.4+1/4.6+......+1/x(x+2)
c,Tính tổng: -1/2 . -2/3 . -3/4..........-99/100
3/4.8/9.15/16.............9999/10000
3/4.8/9.15/16......9999/10000
= 3.8.15.....9999/4.9.16......10000
=101/50
3/4.8/9.15/16........624/625
(1+1/3).(1+1/8).(1+1/15)......(1+1/9999)
3/4.8/9.15/16.....624/625
(1+1/3).(1+1/8).(1+1/15).....(1+1/9999)
\(\frac{3}{4}\cdot\frac{8}{9}\cdot\frac{15}{16}\cdot\cdot\cdot\cdot\frac{624}{625}\)
\(=\frac{1.3}{2.2}\cdot\frac{2.4}{3.3}\cdot\frac{3.5}{4.4}\cdot\cdot\cdot\cdot\frac{24.26}{25.25}\)
\(=\frac{1.2.3....24}{2.3.4....25}\cdot\frac{3.4.5....26}{2.3.4....25}\)
\(=\frac{1}{25}\cdot\frac{26}{2}=\frac{26}{50}=\frac{13}{25}\)
\(\left(1+\frac{1}{3}\right)\cdot\left(1+\frac{1}{8}\right)\cdot\left(1+\frac{1}{15}\right)\cdot\cdot\cdot\cdot\left(1+\frac{1}{9999}\right)\)
\(=\frac{4}{3}\cdot\frac{9}{8}\cdot\frac{16}{15}\cdot\cdot\cdot\cdot\frac{10000}{9999}\)
\(=\frac{2.2}{1.3}\cdot\frac{3.3}{2.4}\cdot\frac{4.4}{3.5}\cdot\cdot\cdot\cdot\frac{100.100}{99.101}\)
\(=\frac{2.3.4...100}{1.2.3...99}\cdot\frac{2.3.4...100}{3.4.5...101}\)
\(=\frac{100}{1}\cdot\frac{2}{101}=\frac{200}{101}\)
tinh 3/4.8/9.15/16....9999/10000
gọi số phải tìm là A A
=(1.3).(2.4).(3.5)...(99.101)/
(2².3².4²...100²)
=(1.2.3...99).(3.4.5...101)/
[(1.2.3.4...100)(2.3.4...100)]
=101/(100.2)=101/200
D= 3/4.8/9.15/16. ...... . 9999/10000 =?
D=1.3/2.2 . 2.4/3.3 . 3.5/4.4 ..... 99.101/100.100
D=1.2.3.....99/2.3.4.....100 . 3.4.5.....101/2.3.4.....100
D=1/100 . 101/2
D=101/200