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\(\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+...+\frac{1}{98.100}\)
\(=\frac{1}{2}\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+....+\frac{2}{98.100}\right)\)
\(=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+....+\frac{1}{98}-\frac{1}{100}\right)\)
\(=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{100}\right)=\frac{49}{200}\)
\(\frac{1}{2x4}+\frac{1}{4x6}+...+\frac{1}{96x98}+\frac{1}{98x199}=\frac{2}{2x4}+\frac{2}{4x6}+...+\frac{2}{99x100}\)
\(=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...-\frac{1}{100}\)
\(=\frac{1}{2}-\frac{1}{100}=\frac{49}{100}\)
A x2 = \(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+............+\frac{1}{98}-\frac{1}{100}\)
A x2 = \(\frac{49}{100}\)
A = \(\frac{49}{200}\)
\(A=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{30}+...+\frac{1}{72}+\frac{1}{81}\)
\(A=\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{8\times9}+\frac{1}{81}\)
\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{8}-\frac{1}{9}+\frac{1}{81}\)
\(A=1-\frac{1}{9}+\frac{1}{81}=\frac{73}{81}\)
\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{81}\)
\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{8.9}+\frac{1}{81}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{8}-\frac{1}{9}+\frac{1}{81}\)
\(=1-\frac{1}{9}+\frac{1}{81}\)
\(=\frac{8}{9}+\frac{1}{81}\)
\(=\frac{73}{81}\)
1/2*(2/2*4+2/4*6+...+2/98*100)=1/2*(1/2-1/4+1/4-1/6+...+1/98-1/100)
=1/2*(1/2-1/100)
=1/2*49/100
=49/200
k nha bạn
\(\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+...+\frac{1}{96.98}+\frac{1}{98.100}\)
\(=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{96}-\frac{1}{98}+\frac{1}{98}-\frac{1}{100}\)
\(=\frac{1}{2}-\frac{1}{100}\)
\(=\frac{49}{100}\)
cho mình tròn 1550 nhé bạn
a) \(\left(\frac{4}{3}-\frac{4}{6}\right)+\left(\frac{4}{6}-\frac{4}{9}\right)+\left(\frac{4}{9}-\frac{4}{10}\right)+\left(\frac{4}{12}-\frac{4}{15}\right)\)
\(=\frac{4}{15}-\frac{4}{3}=\frac{-16}{15}\)
C) bạn chỉ ần bỏ các số giống nhau thôi nhé
= 1
b)
Đặt A=\(\frac{1}{2x4}+\frac{1}{4x6}+.........+\frac{1}{98x100}\)
2A=\(\frac{2}{2x4}+\frac{2}{4x6}+.............+\frac{2}{98x100}\)
2A=\(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+..........+\frac{1}{98}-\frac{1}{100}\)
2A=\(\frac{1}{2}-\frac{1}{100}\)
2A=\(\frac{49}{100}\)
A=\(\frac{49}{100}:2\)
A=\(\frac{49}{200}\)
1/3xD=1/(2x4)+1/(4x6)+...+1/(98x100)
2/3xD=2/(2x4)+2/(4x6)+...+1/(98x100)
2/3xD= 1/2-1/4+1/4-1/6+...+1/98-1/100
2/3xD=1/2-1/100
2/3xD=49/100
D=147/200
Ta có : \(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\)
\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+......+\frac{1}{6}-\frac{1}{7}\)
\(=1-\frac{1}{7}=\frac{6}{7}\)
a: Ta có: \(\frac12+\frac16+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\)
\(=\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+\cdots+\frac{1}{6\times7}\)
\(=1-\frac12+\frac12-\frac13+\cdots+\frac16-\frac17=1-\frac17=\frac67\)
b: Ta có: \(\frac{4}{3\times6}+\frac{4}{6\times9}+\cdots+\frac{4}{18\times21}\)
\(=\frac43\times\left(\frac{3}{3\times6}+\frac{3}{6\times9}+\cdots+\frac{3}{18\times21}\right)\)
\(=\frac43\times\left(\frac13-\frac16+\frac16-\frac19+\cdots+\frac{1}{18}-\frac{1}{21}\right)\)
\(=\frac43\times\left(\frac13-\frac{1}{21}\right)=\frac43\times\frac{6}{21}=\frac43\times\frac27=\frac{8}{21}\)
c: \(\frac12+\frac16+\cdots+\frac{1}{110}\)
\(=\frac{1}{1\times2}+\frac{1}{2\times3}+\cdots+\frac{1}{10\times11}\)
\(=1-\frac12+\frac12-\frac13+\cdots+\frac{1}{10}-\frac{1}{11}=1-\frac{1}{11}=\frac{10}{11}\)
d; Sửa đề: \(\frac{1}{2\times4}+\frac{1}{4\times6}+\frac{1}{6\times8}+\cdots+\frac{1}{98\times100}\)
\(=\frac12\times\left(\frac{2}{2\times4}+\frac{2}{4\times6}+\cdots+\frac{2}{98\times100}\right)\)
\(=\frac12\times\left(\frac12-\frac14+\frac14-\frac16+\cdots+\frac{1}{98}-\frac{1}{100}\right)\)
\(=\frac12\times\left(\frac12-\frac{1}{100}\right)=\frac12\times\frac{49}{100}=\frac{49}{200}\)
: Ta có: \(\frac{1}{2} + \frac{1}{6} + \frac{1}{12} + \frac{1}{20} + \frac{1}{30} + \frac{1}{42}\)
\(= \frac{1}{1 \times 2} + \frac{1}{2 \times 3} + \frac{1}{3 \times 4} + \hdots + \frac{1}{6 \times 7}\)
\(= 1 - \frac{1}{2} + \frac{1}{2} - \frac{1}{3} + \hdots + \frac{1}{6} - \frac{1}{7} = 1 - \frac{1}{7} = \frac{6}{7}\)
b: Ta có: \(\frac{4}{3 \times 6} + \frac{4}{6 \times 9} + \hdots + \frac{4}{18 \times 21}\)
\(= \frac{4}{3} \times \left(\right. \frac{3}{3 \times 6} + \frac{3}{6 \times 9} + \hdots + \frac{3}{18 \times 21} \left.\right)\)
\(= \frac{4}{3} \times \left(\right. \frac{1}{3} - \frac{1}{6} + \frac{1}{6} - \frac{1}{9} + \hdots + \frac{1}{18} - \frac{1}{21} \left.\right)\)
\(= \frac{4}{3} \times \left(\right. \frac{1}{3} - \frac{1}{21} \left.\right) = \frac{4}{3} \times \frac{6}{21} = \frac{4}{3} \times \frac{2}{7} = \frac{8}{21}\)
c: \(\frac{1}{2} + \frac{1}{6} + \hdots + \frac{1}{110}\)
\(= \frac{1}{1 \times 2} + \frac{1}{2 \times 3} + \hdots + \frac{1}{10 \times 11}\)
\(= 1 - \frac{1}{2} + \frac{1}{2} - \frac{1}{3} + \hdots + \frac{1}{10} - \frac{1}{11} = 1 - \frac{1}{11} = \frac{10}{11}\)
d; Sửa đề: \(\frac{1}{2 \times 4} + \frac{1}{4 \times 6} + \frac{1}{6 \times 8} + \hdots + \frac{1}{98 \times 100}\)
\(= \frac{1}{2} \times \left(\right. \frac{2}{2 \times 4} + \frac{2}{4 \times 6} + \hdots + \frac{2}{98 \times 100} \left.\right)\)
\(= \frac{1}{2} \times \left(\right. \frac{1}{2} - \frac{1}{4} + \frac{1}{4} - \frac{1}{6} + \hdots + \frac{1}{98} - \frac{1}{100} \left.\right)\)
\(= \frac{1}{2} \times \left(\right. \frac{1}{2} - \frac{1}{100} \left.\right) = \frac{1}{2} \times \frac{49}{100} = \frac{49}{200}\)