A= 4/3 + 9/8 + 16/15 + ......+ 121/120 = ?
Tính nhanh: 4/3 x 9/8 x 16/15 x ... x 121/120
=2x2/1x3 x 3x3/2x4x4/3x5 x ... x 11x11/10x12
=2x2x3x3x4x4x...x11x11/1x3x2x4x3x5x...x10x12
= 2x3x4x...x11)x(2x3x4x...x11)/(1x2x3x4x...x11)/(1x2x3x...x10)x(2x3x4x...x11)
=11x2/1x12
=22/12
=11/6
4/3x9/8x16/15x...x121/120=\(\dfrac{2^2}{1\cdot3}\)x\(\dfrac{3^2}{2\cdot4}\)x\(\dfrac{4^2}{3\cdot5}\)x...x\(\dfrac{11^2}{10\cdot12}\)=\(\dfrac{2}{3}\)x\(\dfrac{11}{10}\)=\(\dfrac{11}{15}\)
4/3x9/8x16/15x...x121/120=\(\dfrac{2^2}{1\cdot3}\)x\(\dfrac{3^2}{2\cdot4}\)x...x\(\dfrac{11^2}{10\cdot12}\)=\(\dfrac{2}{3}\)x\(\dfrac{11}{10}\)=\(\dfrac{11}{15}\)
3/4×8/9×15/16×....×120/121
Giúp mình vs
\(\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.....\frac{120}{121}\)
\(=\frac{2.3.4......10}{2.3.4.....11}.\frac{3.4.5.....12}{2.3.4.....11}\)
\(=\frac{1}{11}.6=\frac{6}{11}\)
Tính nhanh
4/3*9/8*16/15*25/24*....*121/120*144/143
\(\frac{4}{3}.\frac{9}{8}.\frac{16}{15}.\frac{25}{24}...\frac{121}{120}.\frac{144}{143}\)
\(=\frac{2.2}{1.3}.\frac{3.3}{2.4}.\frac{4.4}{3.5}.\frac{5.5}{4.6}...\frac{11.11}{10.12}.\frac{12.12}{11.13}\)
\(=\frac{2.2.3.3.4.4.5.5...11.11.12.12}{1.3.2.4.3.5.4.6...10.12.11.13}\)
\(=\frac{\left(2.3.4.5...11.12\right).\left(2.3.4.5...11.12\right)}{\left(1.2.3.4...10.11\right).\left(3.4.5.6...12.13\right)}\)
\(=\frac{12.2}{1.13}\)
\(=\frac{24}{13}\)
( Dấu \(.\)là dấu \(\times\)nha )
\(B=\frac{3}{4}\cdot\frac{8}{9}\cdot\frac{15}{16}\cdot...\cdot\frac{120}{121}\)
Giúp mk vs
Ta có:\(B=\frac{1.3}{2.2}x\frac{2.4}{3.3}x\frac{3.5}{4.4}x...x\frac{10.12}{11.11}\)
\(=\frac{1.2.3.4.5.6.7.8.9.10}{2.3.4.5.6.7.8.9.10.11}x\frac{3.4.5.6.7.8.9.10.11.12}{2.3.4.5.6.7.8.9.10.11}\)
\(=\frac{1}{11}x6\)
\(=\frac{6}{11}\)
Ai thấy đúng k nha.
a,1\(\frac{11}{12}\) + 5/12*(4/5 - 1/10) :5/12
b, 3/4*8/9*15/16*24/15*35/36*48/49*63/64*80/81*99/100*120/121
5-5/3+5/9-5/27/8-8/3+8/9-8/27:15-15/11+15/121/16-16/11+16/121
5-5/3+5/9-5/27 15-15/11+15/121
____________ : ________________
8-8/3+8/9-8/27 16-16/11+16/121
D = (1+1/2) x (1+1/3) x (1+1/4) x ... x (1+1/2017)
E = 3/4 x 8/9 x 15/16 x ... x 120/121
1tk cho câu trả lời đúng nhé ! ^^
\(\frac{5-\frac{5}{3}+\frac{5}{9}-\frac{5}{27}}{8-\frac{8}{3}+\frac{8}{9}-\frac{8}{27}}:\frac{15-\frac{15}{11}+\frac{15}{121}}{16-\frac{16}{11}+\frac{16}{121}}\)
\(\frac{5-\frac{5}{3}+\frac{5}{9}-\frac{5}{27}}{8-\frac{8}{3}+\frac{8}{9}-\frac{8}{27}}:\frac{15-\frac{15}{11}+\frac{15}{121}}{16-\frac{16}{11}+\frac{16}{121}}\)
\(=\frac{5\left(1-\frac{1}{3}+\frac{1}{9}-\frac{1}{27}\right)}{8\left(1-\frac{1}{3}+\frac{1}{9}-\frac{1}{27}\right)}:\frac{15\left(1-\frac{1}{11}+\frac{1}{121}\right)}{16\left(1-\frac{1}{11}+\frac{1}{121}\right)}\)
\(=\frac{5}{8}:\frac{15}{16}\)
\(=\frac{2}{3}\)