Tính \(A=\left(1-\frac{1}{4}\right)\left(1-\frac{1}{9}\right)\left(1-\frac{1}{16}\right)...\left(1-\frac{1}{900}\right)\)
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B
21 tháng 8 2017
x. (x^2)^3 = x^5
x^7 ≠ x^5
Nếu,
x^7 - x^5 = 0
mủ lẻ nên phương trình có 3 nghiệm
Đáp số:
x = -1
hoặc
x = 0
hoặc
x = 1
DP
21 tháng 8 2017
a, \(\left(1-\frac{1}{4}\right)\cdot\left(1-\frac{1}{9}\right)\cdot\left(1-\frac{1}{16}\right)\cdot\left(1-\frac{1}{25}\right)\cdot\left(1-\frac{1}{36}\right)\)
\(=\frac{3}{4}\cdot\frac{8}{9}\cdot\frac{15}{16}\cdot\frac{24}{25}\cdot\frac{35}{36}\)
\(=\frac{1.3}{2.2}\cdot\frac{2.4}{3.3}\cdot\frac{3.5}{4.4}\cdot\frac{4.6}{5.5}\cdot\frac{5.7}{6.6}\)
\(=\frac{1.2.3.4.5}{2.3.4.5.6}\cdot\frac{3.4.5.6.7}{2.3.4.5.6}=\frac{1}{6}\cdot\frac{7}{2}\)
\(=\frac{7}{12}\)
b, \(\left(2-\frac{3}{2}\right)\cdot\left(2-\frac{4}{3}\right)\cdot\left(2-\frac{5}{4}\right)\cdot\left(2-\frac{6}{5}\right)\)
\(=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot\frac{4}{5}=\frac{1.2.3.4}{2.3.4.5}\)
\(=\frac{1}{5}\)
MT
13 tháng 8 2015
\(A=\left(\frac{1}{4}-1\right)\left(\frac{1}{9}-1\right)\left(\frac{1}{16}-1\right)\left(\frac{1}{25}-1\right)....\left(\frac{1}{121}-1\right)\)
\(=\frac{-3}{4}.\frac{-8}{9}.\frac{-15}{16}.\frac{-24}{25}....\frac{-120}{121}\)
\(=\left[\left(-1\right)\left(-1\right)\left(-1\right)\left(-1\right)....\left(-1\right)\left(10\right)\text{thừa số -1 }\right].\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}...\frac{10.12}{11.11}\)
\(=\frac{1.12}{2.11}=\frac{6}{11}\)
9 tháng 11 2016
\(A=\left(\frac{1}{4}-1\right)\left(\frac{1}{9}-1\right)\left(\frac{1}{16}-1\right)...\left(\frac{1}{196}-1\right)\)
\(A=\frac{-3}{2.2}.\frac{-8}{3.3}.\frac{-15}{4.4}...\frac{-195}{14.14}\)
\(A=-\left(\frac{3}{2.2}.\frac{8}{3.3}.\frac{15}{4.4}...\frac{195}{14.14}\right)\) (có 13 thừa số, môi thừa số là âm nên kết quả là âm)
\(A=-\left(\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}...\frac{13.15}{14.14}\right)\)
\(A=-\left(\frac{1.2.3...13}{2.3.4...14}.\frac{3.4.5...15}{2.3.4...14}\right)\)
\(A=-\left(\frac{1}{14}.\frac{15}{2}\right)=\frac{-15}{28}\)
HP
19 tháng 5 2016
\(S=\left(\frac{1}{4}-1\right).\left(\frac{1}{9}-1\right).\left(\frac{1}{16}-1\right)...\left(\frac{1}{81}-1\right).\left(\frac{1}{100}-1\right)\)
\(S=\frac{-3}{4}.\frac{-8}{9}.\frac{-15}{16}........\frac{-80}{81}.\frac{-99}{100}\)
\(-S=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}......\frac{80}{81}.\frac{99}{100}\)
\(-S=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}........\frac{8.10}{9.9}.\frac{9.11}{10.10}\)
\(-S=\frac{1.3.2.4.3.5........8.10.9.11}{2.2.3.3.4.4.......9.9.10.10}\)
\(-S=\frac{\left(1.2.3......8.9\right).\left(3.4.5.......10.11\right)}{\left(2.3.4.......9.10\right).\left(2.3.4........9.10\right)}\)\(=\frac{1}{10}.\frac{11}{2}=\frac{11}{20}=>S=\frac{-11}{20}\)
=\(\frac{3}{4}\cdot\frac{8}{9}\cdot\frac{15}{16}...\cdot\frac{899}{900}=\frac{1.3}{2.2}\cdot\frac{2.4}{3.3}\cdot\frac{3.5}{4.4}...\cdot\frac{29\cdot31}{30\cdot30}=\frac{1.2.3.4...29\cdot3.4.5...30.31}{2.2.3.3.4.4...30.30}=\frac{1.31}{2.30}=\frac{31}{60}\)
\(A=\frac{3}{2^2}.\frac{8}{3^2}.\frac{15}{4^2}....\frac{899}{30^2}=\frac{\left(1.3\right).\left(2.4\right).\left(3.5\right)...\left(29.31\right)}{\left(2.3.4...30\right).\left(2.3.4...30\right)}=\frac{\left(1.2....29\right).\left(3.4.5...31\right)}{\left(2.3.4...30\right).\left(2.3.4..30\right)}=\frac{1.31}{30.2}=\frac{31}{60}\)