3/4x8/9x15/16x...x9999/10000
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N
20 tháng 3 2018
= 3/4 x 8/9 x 15/16 x ... x 9999/10000
= 3 x 8 x 15 x ... x 9999/ 4 x 9 x 16 x ... x 10000
= (1 x 3) x (2 x 4) x (3 x 5) x ... x (99 x 101)/ (2 x 2) x (3 x 3) x (4 x 4) x ... x (100 x 100)
= (1 x 2 x 3 x ... x 99) x (3 x 4 x 5 x ... x 101)/ (2 x 3 x 4 x ... x 100) x (2 x 3 x 4 x ... x 100)
= (1 x 2 x 3 x ... x 99) x (3 x 4 x 5 x ... x 101)/ (2 x 3 x 4 x ... x 100) x (2 x 3 x 4 x ... x 100)
= 1x 101/ 100 x 2
= 101/200
CHÚC BN HOK TỐT ^^
TL
2
1 tháng 5 2016
\(\frac{1\cdot3}{2\cdot2}\cdot\frac{2\cdot4}{3\cdot3}\cdot\frac{3\cdot5}{4\cdot4}\cdot...\cdot\frac{99\cdot101}{100\cdot100}\)
\(\frac{1\cdot101}{2\cdot100}\)
\(\frac{101}{200}\)
30 tháng 3 2015
TA CÓ ;
\(A=\frac{3}{4}.\frac{8}{9}...\frac{2499}{2500}\)
\(A=\frac{1.3}{2.2}.\frac{2.4}{3.3}...\frac{49.51}{50.50}\)
\(A=\frac{1.3.2.4...49.51}{2.2.3.3...50.50}\)
\(A=\frac{\left(1.2...49\right).\left(3.4...51\right)}{\left(2.3...50\right).\left(2.3...50\right)}\)
\(A=\frac{1.51}{50.2}=\frac{51}{100}\)
VẬY \(A=\frac{51}{100}\)
S
12 tháng 7 2018
\(B=\frac{3}{4}\cdot\frac{8}{9}\cdot\frac{15}{16}\cdot\cdot\cdot\cdot\frac{2499}{2500}=\frac{1.3}{2.2}\cdot\frac{2.4}{3.3}\cdot\frac{3.5}{4.4}\cdot\frac{49.51}{50.50}\)
\(=\frac{1.2.3....49}{2.3.4...50}\cdot\frac{3.4.5...51}{2.3.4...50}=\frac{1}{50}\cdot\frac{51}{2}=\frac{51}{100}\)
VD
12 tháng 7 2018
A= 3/4x8/9x15/16x.......x 2499/2500
A=\(\frac{3}{4}x\frac{2.4}{3.3}x\frac{3.5}{4.4}x...x\frac{49.51}{50.50}\)
A=\(\frac{3x2x4x3x5x...x49x51}{4x3x3x4x4x...x50x50}\)
A=\(\frac{2x51}{4x50}\)
A=\(\frac{51}{100}\)
VT
12 tháng 7 2018
A= \(=\frac{3\times1}{2\times2}\times\frac{4\times2}{3\times3}\times\frac{3\times5}{4\times4}\times....\times\frac{49\times51}{50\times50}\)
\(=\frac{3\times1\times4\times2\times3\times5\times....\times49\times51}{2\times2\times3\times3\times4\times4\times....\times50\times50}\)
xong loai di nhung so o dang trc va nhan vs 51/50 va ra kq
xin loi vik ko lam het vik qua ban mong chon mik
TA
25 tháng 5 2021
`3/4 xx 8/9 xx 15/16 xx 24/25 xx 35/36`
`= (3xx8xx15xx24xx35)/(4xx9xx16xx25xx36)`
`=(3xx4xx2xx5xx3xx4xx6xx7xx5)/(4xx3xx3xx4xx4xx5xx5xx6xx6)`
`=(2xx7)/(4xx6)`
`=(2xx7)/(2xx2xx6)`
`=7/12`
J
25 tháng 5 2021
\(\dfrac{3}{4}\times\dfrac{8}{9}\times\dfrac{15}{16}\times\dfrac{24}{25}\times\dfrac{35}{36}\)
= \(\dfrac{3\times8\times15\times24\times35}{4\times9\times16\times25\times36}\)
= \(\dfrac{3\times\left(2\times4\text{}\text{}\right)\times\left(3\times5\right)\times\left(6\times4\right)\times\left(5\times7\right)}{4\times\left(3\times3\right)\times\left(4\times4\right)\times\left(5\times5\right)\times\left(6\times6\right)}\)
=\(\dfrac{2\text{}\text{}\times3\times6\times\left(5\times7\right)}{3\times4\times5\times\left(6\times6\right)}\)
=\(\dfrac{\text{}\text{}7}{2\times6}\)= \(\dfrac{7}{12}\)
NM
1
AH
Akai Haruma
Giáo viên
27 tháng 9 2023
Lời giải:
\(\frac{3}{4}\times \frac{8}{9}\times \frac{15}{16}\times ....\times \frac{99}{100}\)
\(=\frac{3\times 8\times 15\times ....\times 99}{4\times 9\times 16\times ....\times 100}\)
\(=\frac{(1\times 3)\times (2\times 4)\times (3\times 5)\times ...\times (9\times 11)}{2\times 2\times 3\times 3\times 4\times 4\times ....\times 10\times 10}\)
\(=\frac{(1\times 2\times 3\times ...\times 9)\times (3\times 4\times 5\times ....\times 11)}{(2\times 3\times 4\times....\times 10)\times (2\times 3\times 4\times ...\times 10)}\)
\(=\frac{1\times 2\times 3\times ....\times 9}{2\times 3\times 4\times ....\times 10}\times \frac{3\times 4\times 5\times ...\times 11}{2\times 3\times 4\times ...\times 10}\)
\(=\frac{1}{10}\times \frac{11}{2}=\frac{11}{20}\)
= 3/4 x 8/9 x 15/16 x ... x 9999/10000
= 3 x 8 x 15 x ... x 9999/ 4 x 9 x 16 x ... x 10000
= (1 x 3) x (2 x 4) x (3 x 5) x ... x (99 x 101)/ (2 x 2) x (3 x 3) x (4 x 4) x ... x (100 x 100)
= (1 x 2 x 3 x ... x 99) x (3 x 4 x 5 x ... x 101)/ (2 x 3 x 4 x ... x 100) x (2 x 3 x 4 x ... x 100)
= 1x 101/ 100 x 2
= 101/200
= 3/4 x 8/9 x 15/16 x ... x 9999/10000
= 3 x 8 x 15 x ... x 9999/ 4 x 9 x 16 x ... x 10000
= (1 x 3) x (2 x 4) x (3 x 5) x ... x (99 x 101)/ (2 x 2) x (3 x 3) x (4 x 4) x ... x (100 x 100)
= (1 x 2 x 3 x ... x 99) x (3 x 4 x 5 x ... x 101)/ (2 x 3 x 4 x ... x 100) x (2 x 3 x 4 x ... x 100)
= 1x 101/ 100 x 2
= 101/200
tích nha