Tính giá trị biểu thức
\(\left(\frac{1}{16}-1\right).\left(\frac{1}{25}-1\right).\left(\frac{1}{36}-1\right).....\left(\frac{1}{10000}-1\right)\)
Những câu hỏi liên quan
tính giá trị của biểu thức M=\(1+\frac{1}{2}.\left(1+2\right)+\frac{1}{3}.\left(1+2+3\right)+\frac{1}{4}.\left(1+2+3+4\right)+...+\frac{1}{16}.\left(1+2+3+...+16\right)\)
TÍNH GIÁ TRỊ BIỂU THỨC
\(\left(1-\frac{1}{28}\right).\left(1-\frac{1}{36}\right).\left(1-\frac{1}{45}\right)......\left(1-\frac{1}{153}\right)\)
Giúp mình nhé. OLM DUYỆT ĐI
=1*(1/28-1/36-1/45-1/153)
=1*125/4284
=125/4284
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tính
\(K=\left(\frac{1}{4}-1\right).\left(\frac{1}{9}-1\right).\left(\frac{1}{16}-1\right).\left(\frac{1}{25}-1\right).\left(\frac{1}{36}-1\right).\left(\frac{1}{49}-1\right).\left(\frac{1}{64}-1\right).\left(\frac{1}{81}-1\right).\left(\frac{1}{100}-1\right)\)
Tính giá trị của biểu thức sau: \(M=\frac{-1,2:\left(1\frac{3}{5}.1,25\right)}{0,64-\frac{1}{25}}+\frac{\left(1,08-\frac{2}{25}\right):\frac{4}{7}}{\left(5\frac{5}{9}-\frac{9}{4}\right).\frac{36}{17}+}+0,6.0,5:\frac{2}{3}\)
Tính giá trị biểu thức: A=\(\frac{\left(1+17\right).\left(1+\frac{17}{2}\right).\left(1+\frac{17}{3}\right)....\left(1+\frac{17}{19}\right)}{\left(1+19\right).\left(1+\frac{19}{2}\right).\left(1+\frac{19}{3}\right)...\left(1+\frac{19}{17}\right).}\)
Tính các tích sau:
a)\(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.....\frac{9999}{10000}\)
b)\(B=\left(1-\frac{1}{21}\right).\left(1-\frac{1}{28}\right).\left(1-\frac{1}{36}\right)......\left(1-\frac{1}{1326}\right)\)
c)\(C=\left(1+\frac{1}{1.3}\right).\left(1+\frac{1}{2.4}\right).\left(1+\frac{1}{3.5}\right)....\left(1+\frac{1}{99.101}\right)\)
Tính\
\(\left(\frac{1}{16}-1\right).\left(\frac{1}{25}-1\right).\left(\frac{1}{36}-1\right)......\left(\frac{1}{100}-1\right)\))
Xin lỗi bn mk bị nhầm
\(\frac{3.5}{4^2}.\frac{4.6}{5^2}.\frac{5.7}{6^2}...\frac{9.11}{10^2}\)
= \(\frac{3.4.5...9}{4.5.6...9.10}.\frac{5.6...9.10.11}{4.5.6...9.10}=\frac{3}{10}.\frac{11}{4}=\frac{33}{40}\)
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\(\left(\frac{1}{16}-1\right)\left(\frac{1}{25}-1\right)\left(\frac{1}{36}-1\right)...\left(\frac{1}{100}-1\right)\)
= \(\frac{15}{16}.\frac{24}{25}.\frac{35}{36}...\frac{99}{100}\)
= \(\frac{3.5}{4^2}.\frac{4.6}{5^2}.\frac{5.7}{6^2}...\frac{9.11}{10^2}\)
= \(\frac{3.4.5...9.10}{4.5...9.10}.\frac{5.6.7..9.10.11}{4.5.6...9.10}=3.\frac{11}{4}=\frac{33}{4}\)
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\(\left(1+\frac{1}{1.3}\right)\left(1+\frac{1}{2.4}\right)\left(1+\frac{1}{3.5}\right)\left(1+\frac{1}{4.6}\right)...\left(1+\frac{1}{2013.2015}\right)\)
Hãy tính giá trị biểu thức
\(\left(1+\frac{1}{1\cdot3}\right)\left(1+\frac{1}{2\cdot4}\right)\left(1+\frac{1}{3\cdot5}\right)...\left(1+\frac{1}{2013\cdot2015}\right)\)
\(=\frac{4}{1\cdot3}\cdot\frac{9}{2\cdot4}\cdot\frac{16}{3\cdot5}\cdot...\cdot\frac{4056196}{2013\cdot2015}\)
\(=\frac{\left(2\cdot2\right)\left(3\cdot3\right)\left(4\cdot4\right)...\left(2014\cdot2014\right)}{\left(1\cdot3\right)\left(2\cdot4\right)\left(3\cdot5\right)...\left(2013\cdot2015\right)}\)
\(=\frac{\left(2\cdot3\cdot4\cdot...\cdot2014\right)\left(2\cdot3\cdot4\cdot...\cdot2014\right)}{\left(1\cdot2\cdot3\cdot...\cdot2013\right)\left(3\cdot4\cdot5\cdot...\cdot2015\right)}\)
\(=\frac{2014\cdot2}{1\cdot2015}\)
\(=\frac{4028}{2015}\)
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Tính giá trị biểu thức: A=\(\frac{\left(1+17\right)\times\left(1+\frac{17}{2}\right)\times\left(1+\frac{17}{3}\right)....\left(1+\frac{17}{19}\right)}{\left(1+19\right)\times\left(1+\frac{19}{2}\right)\times\left(1+\frac{19}{3}\right)....\left(1+\frac{19}{17}\right)}\)