1/2*3 +1/3*4 + ...+ 1/a(a+1)=49/100
=1/2-1/3+1/3-1/4+1/5-1/6+...+1/a-1/(a+1)
=1/2-1/(a+1)=49/100
50/100 -49/100=1/(a+1)
1/100=1(a+1)
a+1=100
a=99
Tìm số tự nhiên biết : \(\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+...+\frac{1}{a\times\left(a+1\right)}=\frac{49}{100}\)
Trả lời : a =................
Tìm \(x\):
\(\left(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+.....\frac{1}{2009\times2010}\right)\times x=2009\)
Tìm x, biết: \(x\times\left(44+\frac{2010}{1\times2}+\frac{2006}{2\times3}+\frac{2000}{3\times4}+...+\frac{32}{44\times45}\right)=\frac{44}{45}\)
Tính nhanh :
A = \(\frac{1,25\times10\div0,25\times24,4\times2}{6,1\times2\times6,25\times4\div0,5}+\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right).........\left(1-\frac{1}{19}\right)\times\left(1-\frac{1}{20}\right)\)
1.Tính nhanh
a,\(\frac{1}{1\times4}+\frac{1}{4\times7}+............+\frac{1}{97\times100}\)
b,\(\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times...........\times\frac{99}{100}\)
c,\(\frac{3}{4}\times\frac{8}{9}\times\frac{15}{16}\times...........\times\frac{99}{100}\)
d,\(\left(\frac{1}{2}+1\right)\times\left(\frac{1}{3}+1\right)\times\left(\frac{1}{4}+1\right)\times............\times\left(\frac{1}{99}+1\right)\)
e,\(\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)\times..........\times\left(1-\frac{1}{100}\right)\)
Tìm x biết \(\left(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}\right)\times10-x=0\)
Tính nhanh : \(\frac{1}{8}\div12,5\%+\left(\frac{1\times2\times3+6\times4\times2}{5\times3\times1+5\times15\times25}+\frac{1}{2}\div50\%\right)-\left(\frac{1}{16}\div6,25\%+\frac{3+2+1+2+4+6}{1+3+5+25+15+5}\right)-\frac{1}{4}\div25\%\)
Tính nhanh:\(\frac{\left(1+2\right)\times3}{\left(2+3\right)\times4}+\frac{\left(2+3\right)\times4}{\left(3+4\right)\times5}+...+\frac{\left(999+1000\right)\times1001}{\left(1000+1001\right)\times1002}+\frac{\left(1000+1001\right)\times1002}{\left(1001+1002\right)\times1003}\)
Cho biểu thức A= \(\frac{1}{1\times2\times3}\)+ \(\frac{1}{2\times3\times4}\)+ \(\frac{1}{3\times4\times5}\)+...+ \(\frac{1}{18\times19\times20}\). So sánh A với \(\frac{1}{4}\).
