Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+....+\frac{1}{98\times99}+\frac{1}{99\times100}\)
\(=\frac{2-1}{1\times2}+\frac{3-2}{2\times3}+\frac{4-3}{3\times4}+....+\frac{99-98}{98\times99}+\frac{100-99}{99\times100}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\)
\(=1-\frac{1}{100}\)
\(=\frac{99}{100}\)
\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{98\cdot99}+\frac{1}{99\cdot100}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)
\(=1-\frac{1}{100}\)
\(=\frac{99}{100}\)
=1-1/2+1/2-1/3+....................+1/99-1/100
=1+(1/2-1/2+1/3-1/3+.............+1/99-1/99)-1/100
=1-1/100
=99/100
A = 1 - 1/2 + 1/2 - 1/3 +.............+ 1/99 - 1/100
= 1 - 1/100 = 99/100
\(B=\dfrac{1}{3}\left(\dfrac{3}{1\cdot4}+\dfrac{3}{4\cdot7}+...+\dfrac{3}{97\cdot100}\right)\)
\(=\dfrac{1}{3}\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+...+\dfrac{1}{97}-\dfrac{1}{100}\right)\)
\(=\dfrac{1}{3}\left(1-\dfrac{1}{100}\right)\)
\(=\dfrac{1}{3}\cdot\dfrac{99}{100}=\dfrac{33}{100}\)
\(3\times B=\dfrac{3}{1\times4}+\dfrac{3}{4\times7}+....+\dfrac{3}{97\times100}\)
\(3\times B=1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+...+\dfrac{1}{97}-\dfrac{1}{100}\)
\(3\times B=1-\dfrac{1}{100}=\dfrac{99}{100}\)
\(B=\dfrac{33}{100}\)
a) \(\frac{4}{7}=\frac{16}{28}\)
\(\frac{9}{12}=\frac{3}{4}=\frac{21}{28}\)
b) \(\frac{13}{12}=\frac{39}{36}\)
\(\frac{19}{18}=\frac{38}{36}\)
c) \(\frac{1}{5}=\frac{2}{10}\)
d) \(\frac{1}{3}=\frac{21}{63}\)
\(\frac{2}{7}=\frac{18}{63}\)
\(\frac{4}{9}=\frac{28}{63}\)
a/ 4/7 = 1-3/7 và 9/12 = 1-3/12
vì 3/7>3/12 nên 1-3/7<1-3/12
Vậy 4/7<9/12
b/ 13/12 = 1+1/12 và 19/18 = 1+1/18
Vì 1/12>1/18 nên 13/12>19/18
\(\frac{2}{1X2}+\frac{2}{2X3}+\frac{2}{3X4}+...+\frac{2}{98X99}+\frac{2}{99X100}\)
\(2X\left(\cdot\frac{1}{1X2}+\frac{1}{2X3}+...+\frac{1}{98X99}+\frac{1}{99X100}\right)\)
\(2X\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\right)\)
\(2X\left(1-\frac{1}{100}\right)\)
\(2X\frac{99}{100}\)
\(\frac{99}{50}\)
1/2+1/4+1/8+1/10
=(1/2+1/4+1/8)+1/10
=(4/8+2/8+1/8)+1/10
=7/8+1/10
=39/40
10 + 1/12 × 100
= 10 + 25/3
= 30/3 + 25/3
= 55/3.
\(10+\frac{1}{12}\cdot100=100+\frac{25}{3}\)
\(=\frac{300}{3}+\frac{25}{3}\)
\(=\frac{325}{3}\)