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\(A=\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+\frac{1}{1+2+3+4+5}\)
\(A=\frac{1}{\left(1+2\right).2:2}+\frac{1}{\left(1+3\right).3:2}+\frac{1}{\left(1+4\right).4:2}+\frac{1}{\left(1+5\right).5:2}\)
\(A=\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+\frac{2}{5.6}\)
\(A=2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}\right)\)
\(A=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\right)\)
\(A=2\left(\frac{1}{2}-\frac{1}{6}\right)\)
\(A=2.\frac{1}{3}=\frac{2}{3}\)
0,75 \(\times\) \(\dfrac{4}{3}\) + \(\dfrac{5}{13}\) : \(\dfrac{1}{26}\)
= \(\dfrac{3}{4}\) \(\times\) \(\dfrac{4}{3}\) + \(\dfrac{5}{13}\) \(\times\) \(\dfrac{26}{1}\)
= 1 + 10
= 11
1+2+3+4+5+6+7+8+9+10
=3+3+4+5+6+7+8+9+10
=6+4+5+6+7+8+9+10
=10+5+6+7+8+9+10
=15+6+7+8+9+10
=21+7+8+9+10
=28+8+9+10
=36+9+10
=45+10
=55
Siêu chi tiết
1-1/3=2/3; 1-1/4=3/4; 1-1/5=4/5....; 1-1/99=98/99
=> A= (2.3.4.5....98):(3.4.5....99)=2/99
Đs: 2/99
ca mau va tu duoc them =4+3=7
tu so la =7:{2-1}*1=7
mau so la=7:{2-1}*2--3=11
vay phan so do =7/11
dap so =7/11
Đặt A=1/1*2+1/2*3+...+1/13*14
=> A=1-1/2+1/2-1/3+...+1/13-1/14
=> A=1-1/14
=> A=13/14