Question

\(\frac{2}{11x16}\)+\(\frac{2}{16x21}\)+.................+\(\frac{2}{61x66}\)

\(\frac{2}{5x7}\)+\(\frac{4}{7x11}\)+\(\frac{3}{11x14}\)+\(\frac{4}{14x18}\)+\(\frac{5}{18x23}\)+\(\frac{7}{23x30}\)

hãy tính nhanh hai phép tính trên

Answer 1

a) \(\frac{2}{11x16}+\frac{2}{16x21}+...+\frac{2}{61x66}\)

\(=\frac{2}{5}x\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}\right)\)

\(=\frac{2}{5}x\left(\frac{1}{11}-\frac{1}{66}\right)\)

\(=\frac{2}{5}x\frac{5}{66}\)

\(=\frac{1}{33}\)

b) \(\frac{2}{5x7}+\frac{4}{7x11}+\frac{3}{11x14}+\frac{4}{14x18}+\frac{5}{18x23}+\frac{7}{23x30}\)

\(=\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{18}+\frac{1}{18}-\frac{1}{23}+\frac{1}{23}-\frac{1}{30}\)

\(=\frac{1}{5}-\frac{1}{30}\)

\(=\frac{1}{6}\)

Answer 2

a, \(\frac{2}{11\times16}+\frac{2}{16\times21}+...+\frac{2}{61\times66}\)

\(=\frac{2}{5}\times\left(\frac{5}{11\times16}+...+\frac{5}{61\times66}\right)\)

\(=\frac{2}{5}\times\left(\frac{1}{11}-\frac{1}{16}+...+\frac{1}{61}-\frac{1}{66}\right)\)

\(=\frac{2}{5}\times\left(\frac{1}{11}-\frac{1}{66}\right)\)

\(=\frac{2}{5}\times\frac{5}{66}\)

\(=\frac{1}{33}\)

Vậy giá trị của biểu thức trên là : \(\frac{1}{33}\)

b,\(\frac{2}{5\times7}+\frac{4}{7\times11}+\frac{3}{11\times14}+\frac{4}{14\times18}+\frac{5}{18\times23}\)

\(=\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{18}+\frac{1}{18}-\frac{1}{23}\)

\(=\frac{1}{5}-\frac{1}{23}\)

\(=\frac{18}{115}\)

Vậy giá trị của biểu thức trên là \(\frac{18}{115}\)

Answer 3

Sorry phần b nha :

\(\frac{18}{115}+\frac{7}{23\times30}\)

\(=\frac{1}{6}\)

Answer 4

Câu 1:

\(\frac{2}{11.16}+\frac{1}{16.21}+...+\frac{2}{61.66}\)

\(=\frac{2}{5}.\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}\right)\)

\(=\frac{2}{5}.\left(\frac{1}{11}-\frac{1}{66}\right)\)

\(=\frac{2}{5}.\frac{5}{66}\)

\(=\frac{10}{330}\)

Câu 2:

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