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\(D=\frac{2}{25.27}+2\left(\frac{1}{10}-\frac{1}{12}+\frac{1}{12}-\frac{1}{14}+...+\frac{1}{48}-\frac{1}{50}\right)\)
\(D=2.\left(\frac{1}{25}-\frac{1}{27}\right)+2\left(\frac{1}{10}-\frac{1}{50}\right)\)
\(D=2.\frac{2}{675}+2.\frac{2}{25}\)
\(D=2.\left(\frac{2}{675}+\frac{2}{25}\right)\)
\(D=2.\frac{56}{675}\)
\(D=\frac{112}{675}\)
Study well
Đặt \(A=\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{16.18}\)
\(A=\frac{4-2}{2.4}+\frac{6-4}{4.6}+\frac{8-6}{6.8}+....+\frac{18-16}{16.18}\)
\(A=\frac{4}{2}.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{16}-\frac{1}{18}\right)\)
\(A=\frac{4}{2}.\left(\frac{1}{2}-\frac{1}{18}\right)\)
\(A=\frac{4}{2}.\frac{4}{9}\)
\(\Rightarrow A=\frac{8}{9}\)
\(\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{16.18}\)
\(=\frac{4}{2}\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{16}-\frac{1}{18}\right)\)
\(=2\left(\frac{1}{2}-\frac{1}{18}\right)\)
\(=2.\frac{4}{9}\)
\(=\frac{8}{9}\)
Từ 1 đến 100 có Số số hạng là :
( 100 -1 ) : 1 + 1 = 100 ( số )
=> TỪ 1/1 -> 100/100 có 100 số
TA có 1/1 + 2/2 + 3/3 + ... + 99/99 + 100/100
= 1 + 1 + 1 + ... + 1
=> có 100 số 1
= 100 x 1 = 100
Các bạn t i ck mk nếu đúng nha !
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) \(\frac{2}{5x7}+\frac{4}{7x11}+\frac{3}{11x14}+\frac{4}{14x18}+\frac{5}{18x23}+\frac{7}{23x30}\)
\(=\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{18}+\frac{1}{18}-\frac{1}{23}+\frac{1}{23}-\frac{1}{30}\)
\(=\frac{1}{5}-\frac{1}{30}\)
\(=\frac{1}{6}\)
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 \(\frac{18}{115}\)
a ) \(5\frac{3}{4}:3+2\frac{1}{4}.\frac{1}{3}-\frac{3}{8}=\frac{23}{4}:\frac{3}{1}+\frac{9}{4}.\frac{1}{3}=\frac{23}{12}+\frac{3}{4}=\frac{8}{3}\)
b ) \(\frac{3}{5}:\frac{5}{6}:\frac{6}{7}:\frac{7}{8}+\frac{7}{8}+\frac{2}{5}+\frac{23}{35}=\frac{3.6.7.8}{5.5.6.7}+\frac{7}{8}+\frac{2}{5}+\frac{23}{35}=\frac{24}{25}+\frac{7}{8}+\frac{2}{5}+\frac{23}{35}=\frac{4049}{1400}\)