Đặt A = \(\frac{\frac{1}{2}}{1+2}+\frac{\frac{1}{2}}{1+2+3}+...+\frac{\frac{1}{2}}{1+2+3+....+100}\)

         = \(\frac{1}{2}\left(\frac{1}{2.3:2}+\frac{1}{3.4:2}+\frac{1}{4.5:2}+...+\frac{1}{100.101:2}\right)\)

         = \(\frac{1}{2}\left(\frac{2}{2.3}+\frac{2}{3.4}+....+\frac{2}{100.101}\right)\)

         = \(\frac{1}{2}.2\left(\frac{1}{2.3}+\frac{1}{3.4}+....+\frac{1}{100.101}\right)\)

         = 1\(\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{100}-\frac{1}{101}\right)\)

         = \(\frac{1}{2}-\frac{1}{101}=\frac{101}{202}-\frac{2}{202}=\frac{99}{202}\)

Ghi đầy đủ nha

bn có thể ghi rõ ràng đc ko?

a)\(-\dfrac{3}{7}+\dfrac{5}{13}+\dfrac{3}{7}\) 

=\(\left(-\dfrac{3}{7}+\dfrac{3}{7}\right)+\dfrac{5}{13}\) 

=\(0+\dfrac{5}{13}\) 

=\(\dfrac{5}{13}\)

\(\left(1+1\frac{1}{4}+1\frac{1}{2}+1\frac{3}{4}+2+2\frac{1}{4}+2\frac{1}{2}+2\frac{3}{4}+...+4\frac{3}{4}\right):23\)

= \(\left(\frac{2}{2}+\frac{5}{4}+\frac{3}{2}+\frac{7}{4}+\frac{4}{2}+\frac{9}{4}+\frac{5}{2}+\frac{11}{4}+...+\frac{19}{4}\right):23\)

= \(\left(\frac{4}{4}+\frac{5}{4}+\frac{6}{4}+\frac{7}{4}+\frac{8}{4}+\frac{9}{4}+\frac{10}{4}+\frac{11}{4}+...+\frac{19}{4}\right):23\)

= \(\left(\frac{4+5+6+7+8+9+10+11+...+19}{4}\right):23\)

= \(\left(\frac{\left(19-4\right):1+1x\left(19+4\right):2}{4}\right):23\)

=  \(46:23\)

= \(2\)

1/1+2 + 1/1+2+3 +1/1+2+3+4 +...+1/1+2+3+...+50

Ta có 2/2(1+2)+2/2(1+2+3)+...+2/2(1+2+...+50)

=2/6+2/12+2/20+...+2/2550

=2/2.3+2/3.4+...+2/50.51

=2(1/2.3+1/3.4+...+1/50.51)

=2(1/1-1/2+1/2-...+1/50-1/51)

=2.(1-1/51)

=2.50/51=100/51

Thua k câu hỏi trước của mình nhé

k là k đánh lộn

bạn giải giúp mk bài này nhé

cầu xin bạn tại mk đang cần gấp huhuhu