\(\frac{4}{1\times3}+\frac{4}{3\times5}+\frac{4}{5\times7}+...+\frac{4}{11\times13}=?\)
a,\(\frac{3^{10}\times(-5)^{21}}{\left(-5\right)^{20}\times3^{12}}\)
b,\(\frac{\left(-11\right)^5\times13^7}{11^5\times13^8}\)
c,\(\frac{2^{10}\times3^{10}-2^{10}\times3^9}{2^9\times3^{10}}\)
d,\(\frac{5^{11}\times7^{12}+5^{11}\times7^{11}}{5^{12}\times7^{12}+9\times5^{11}\times7^{11}}\)
Bài trên là bài rút gon phân số
\(a)\frac{3^{10}.\left(-5\right)^{21}}{\left(-5\right)^{20}.3^{12}}=\frac{-5}{3^2}=\frac{-5}{9}\)
\(b)\frac{-11.13^7}{11^5.13^8}=\frac{-1}{11^4.13}\) (Bạn xem thử xem có sai đề không nhé)
\(c)\frac{2^{10}.3^{10}-2^{10}.3^9}{2^9.3^{10}}=\frac{2^{10}.3^9\left(3+1\right)}{2^9.3^{10}}=\frac{2.4}{3}=\frac{8}{3}\)
\(d)\frac{5^{11}.7^{12}+5^{11}.7^{11}}{5^{12}.7^{12}+9.5^{11}.7^{11}}=\frac{5^{11}.7^{11}\left(7+1\right)}{5^{11}.7^{11}\left(5.4+9\right)}=\frac{8}{20+9}=\frac{8}{29}\)
\(a)\frac{3^{10}\cdot\left(-5\right)^{21}}{\left(-5\right)^{20}\cdot3^{12}}=\frac{-5}{3^2}=\frac{-5}{9}\)
\(b)\frac{\left(-11\right)\cdot13^7}{11^5\cdot13^8}=\frac{-1}{11^4\cdot13}=\frac{-1}{14641\cdot13}=\frac{-1}{190333}\)
\(c)\frac{2^{10}\cdot3^{10}-2^{10}\cdot3^9}{2^9\cdot3^{10}}=\frac{2^{10}\left(3^{10}-3^9\right)}{2^9\cdot3^{10}}=\frac{2^{10}\cdot3^9\left(3-1\right)}{2^9\cdot3^{10}}=\frac{2^{10}\cdot3^9\cdot2}{2^9\cdot3^{10}}=\frac{2\cdot2}{3}=\frac{4}{3}\)
tính :\(\frac{1}{1\times2\times3}+\frac{1}{2\times3\times4}+\frac{1}{3\times4\times5}+\frac{1}{4\times5\times6}+\frac{1}{5\times6\times7}+\frac{1}{6\times7\times8}+\frac{1}{7\times8\times9}+\frac{1}{8\times9\times10}\)
\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{8.9.10}=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}\right)+\frac{1}{2}.\left(\frac{1}{2.3}-\frac{1}{3.4}\right)+...+\frac{1}{2}.\left(\frac{1}{8.9}-\frac{1}{9.10}\right)\)
\(=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{8.9}-\frac{1}{9.10}\right)\)
\(\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{9.10}\right)=\frac{1}{2}.\frac{22}{45}=\frac{11}{45}\)
\(\frac{9^8\times3-9^9}{9^8\times5+9^8\times7}\div\frac{11^4\times6-11^5}{11^4-11^5}\div\frac{10^5-10^5\times3}{10^511}\)
\(\left(\frac{4}{1\times3}+\frac{4}{3\times5}+\frac{4}{5\times7}+\frac{4}{7\times9}\right)\times10-x=0\)
(4/1*3+4/3*5+4/5*7+4/7*9)*10-x=0
=4*2/1*3+4*2/3*5+4*2/5*7+4*2/7*9
=1/1+1/3+1/5+1/7+1/9
=1/1-1/9
=8/9
8/9*10-x=0
89-x=0
x=89-0
x=89
Các bạn giúp mk, mk cần gấp!
\(\frac{4}{1\times3}+\frac{4}{3\times5}+\frac{4}{5\times7}+......+\frac{4}{99\times101}\)
\(\frac{4}{1.3}+\frac{4}{3.5}+\frac{4}{5.7}+...+\frac{4}{99.101}\)
\(=2.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{99.101}\right)\)
\(=2.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{101}\right)\)
\(=2.\left(1-\frac{1}{101}\right)\)
\(=2.\frac{100}{101}=\frac{200}{101}\)
Đặt \(A=\frac{4}{1.3}+\frac{4}{3.5}+\frac{4}{5.7}+..+\frac{4}{99.101}\)
\(A=2.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{99.101}\right)\)
\(A=2.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{101}\right)\)
\(A=2.\left(1-\frac{1}{101}\right)\)
\(A=\frac{2.100}{101}=\frac{200}{101}\)
Ủng hộ mk nha !!! ^_^
Ta gọi tổng trên là A
Ta có: A = 4/1x3+4/3x5 + 4/5x7+...+4/99x101
=>A x 2/4 = 2/1x3+2/3x5+2/5x7+...+2/99x101
=1-1/2+1/2-1/3+1/3-1/4+....+1/99+1/101
=1-1/101=100/101
\(\frac{4}{1\times3}+\frac{4}{3\times5}+\frac{4}{5\times7}+...+\frac{4}{2011\times2013}\)
\(\frac{4}{1.3}+\frac{4}{3.5}+........+\frac{4}{2011.2013}\)
\(=2\left(\frac{2}{1.3}+\frac{2}{3.5}+........+\frac{2}{2011.2013}\right)\)
\(=2.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+........+\frac{1}{2011}-\frac{1}{2013}\right)\)
\(=2\left(1-\frac{1}{2013}\right)\)
\(=2.\frac{2012}{2013}\)
\(=\frac{4024}{2013}\)
Giúp mình với!!!!!
Tính:
G=\(\frac{1}{1\times3\times5}+\frac{1}{5\times7\times9}+\frac{1}{9\times11\times13}+...+\frac{1}{49\times51\times53}\)
\(\frac{1}{1x3x5}+\frac{1}{5x7x9}+\frac{1}{9x11x13}+.....+\frac{1}{49x51x53}=\)
\(1-\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}-\frac{1}{9}+.....+\frac{1}{49}-\frac{1}{51}-\frac{1}{53}=\)
\(1-\frac{1}{3}-\frac{1}{7}-....-\frac{1}{51}-\frac{1}{53}=\)
\(\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}+\frac{1}{6\times7}+\frac{1}{7\times8}+\frac{1}{8\times9}+\frac{1}{9\times10}\)
1/2.3+1/3.4+1/4.5+1/5.6+1/6.7+1/7.8+1/8.9+1/9.10
=1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6+1/7-1/7+1/8-1/8+1/9+1/9-1/10
=1/2-1/10
=5/10-1/10
=4/10=2/5
\(\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+\frac{1}{5x6}+\frac{1}{6x7}+\frac{1}{8x9}+\frac{1}{9x10}\)
\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\)
\(\frac{1}{2}-\frac{1}{10}\)
\(\frac{2}{5}\)
= 1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10
= 1/2-0-0-0-0-0-0-0-0-1/10
=1/2 - 1/10
=2/5
tớ trước nhé
Tính \(\frac{1}{3\times5}+\frac{1}{5\times7}+\frac{1}{7\times9}+\frac{1}{9\times11}+\frac{1}{11\times13}\)
SAI HẾT RỒI.........CẦN THÌ TỚ GIẢI LẠI CHO !!
thế này :
= \(\frac{1}{2}\left(\frac{2}{3.5}+\frac{2}{5.7}+......+\frac{2}{11.13}\right)\)
= \(\frac{1}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+....+\frac{1}{11}-\frac{1}{13}\right)\)
= \(\frac{1}{2}\left(\frac{1}{3}-\frac{1}{13}\right)\)
= \(\frac{1}{2}.\frac{10}{39}\)
= \(\frac{5}{39}\)
Vậy kq = \(\frac{5}{39}\)