\(\frac{3}{2^2}\cdot\frac{8}{32}\cdot\frac{15}{4^2}\cdot......\cdot\frac{899}{30^2}\)
Bài 1 : tính
a) \(\frac{3}{2^2}\cdot\frac{8}{3^2}\cdot\frac{15}{4^2}\cdot...\cdot\frac{899}{30^2}\)
b) \(\frac{\left(\frac{3}{4}+\frac{3}{7}-\frac{3}{8}\right)}{\frac{5}{4}+\frac{5}{7}-\frac{5}{8}}\)
Tính:
a, \(\frac{7}{12}+\frac{5}{6}+\frac{1}{4}-\frac{3}{7}-\frac{5}{12}_{ }\)
b, \(\frac{11\cdot3^{22}\cdot3^7-9^{15}}{\left(2\cdot3^{14}\right)^2}\)
c, \(\frac{3}{2^2}\cdot\frac{8}{3^2}\cdot\frac{15}{4^2}\cdot...\cdot\frac{899}{30^2}\)
tính:
A=\(\frac{1^2}{1\cdot2}\cdot\frac{2^2}{2\cdot3}\cdot\frac{3^2}{3\cdot4}\cdot\frac{4^2}{4\cdot5}...\frac{8^2}{8\cdot9}\cdot\frac{9^2}{9\cdot10}\)
B=\(\frac{2^2}{3}\cdot\frac{^{3^2}}{8}\cdot\frac{4^2}{15}\cdot\frac{6^2}{35}\cdot\frac{7^2}{48}\cdot\frac{8^2}{63}\cdot\frac{9^2}{80}\)
a) \(\left(\frac{11}{4}\cdot\frac{-5}{9}-\frac{4}{9}\cdot\frac{11}{4}\right)\cdot\frac{8}{33}\)
b) \(\frac{-1}{4}\cdot\frac{152}{11}+\frac{68}{4}\cdot\frac{-1}{11}\)
c) \(\frac{-2}{3}\cdot\frac{4}{5}+\frac{2}{3}\cdot\frac{3}{5}\)
d) \(\left(\frac{1}{2}-1\right)\cdot\left(\frac{1}{3}-1\right)\cdot\left(\frac{1}{4}-1\right)\cdot....\cdot\left(\frac{1}{100}-1\right)\)
e) \(\frac{3}{2^2}\cdot\frac{8}{3^2}\cdot\frac{15}{4^2}\cdot...\cdot\frac{8^{99}}{30^2}\)
Rút gọn biểu thức A=\(\frac{3}{4}\cdot\frac{8}{9}\cdot\frac{15}{16}\cdot\frac{24}{25}\cdot....\cdot\frac{899}{900}\)ta được A=......
(Nhập kết quả dạng phân số tối giản)
Tìm x
a, \(\left(x-1\right)^{x+2}=\left(x-1\right)^{x+4}\)
b,\(\frac{1}{4}\cdot\frac{2}{6}\cdot\frac{3}{8}\cdot\frac{4}{10}\cdot\frac{5}{12}.....\frac{30}{62}\cdot\frac{31}{64}=2^x\)
1. Tính tổng
\(\frac{1}{2}\cdot\frac{1}{3}\cdot+\frac{1}{3}\cdot\frac{1}{4}+\frac{1}{4}\cdot\frac{1}{5}+\frac{1}{5}\cdot\frac{1}{6}+\frac{1}{6}\cdot\frac{1}{7}+\frac{1}{7}\cdot\frac{1}{8}+\frac{1}{8}\cdot\frac{1}{9}\)
G=\(\frac{2^2}{1\cdot3}\cdot\frac{3^2}{2\cdot4}\cdot\frac{4^2}{3\cdot5}\cdot\cdot\cdot\cdot\frac{50^2}{49.51}\)
H=\(\left(1-\frac{1}{7}\right)\cdot\left(1-\frac{2}{7}\right)\cdot\left(1-\frac{3}{7}\right)\cdot\cdot\cdot\cdot\cdot\left(1-\frac{10}{7}\right)\)
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