Cho S=\(\dfrac{3}{1.4}+\dfrac{3}{4.7}+\dfrac{3}{7.10}+......+\dfrac{3}{40.43}+\dfrac{3}{43.46}\).Hãy chứng tỏ S<1
Mọi người giúp em với ạ. em cảm ơn
Chứng tỏ:
\(\dfrac{200-\left(3+\dfrac{2}{3}+\dfrac{2}{4}+\dfrac{2}{5}+...+\dfrac{2}{100}\right)}{\dfrac{1}{2}+\dfrac{2}{3}+\dfrac{3}{4}+...+\dfrac{99}{100}}\)=2
\(Cho\) \(S=\dfrac{3}{1.4}+\dfrac{3}{4.7}+\dfrac{3}{7.10}+...+\dfrac{3}{n\left(n+1\right)}\)
Chưng minh rằng S<1
trả lời cho mik mấy câu này nhé cảm ơn làm đúng mik tick cho
a) \(4,5:\left[\left(1\dfrac{1}{2}-\dfrac{5}{3}\right)-\dfrac{9}{5}+2,4\right]-\dfrac{1}{7}\)
b) \(4\dfrac{1}{3}:\left(25\%+1,25\right)-6\dfrac{2}{3}\)
c)\(\dfrac{5}{1.4}+\dfrac{5}{4.7}+\dfrac{5}{7.10}+.......+\dfrac{5}{91.94}\)
Chứng minh rằng với mọi số tự nhiên khác 0 ta đều có :
a) \(\dfrac{1}{2.5}+\dfrac{1}{5.8}+\dfrac{1}{8.11}+...+\dfrac{1}{\left(3n-1\right).\left(3n+2\right)}=\dfrac{n}{6n+4}\)
b) \(\dfrac{5}{3.7}+\dfrac{5}{7.11}+\dfrac{5}{11.15}+...+\dfrac{5}{\left(4n-1\right).\left(4n+3\right)}=\dfrac{5n}{4n+3}\)
giúp mk với
tính
a, A = \(\dfrac{3}{2}\) + \(\dfrac{3}{10}\) + \(\dfrac{3}{50}\)+ \(\dfrac{3}{250}\) + \(\dfrac{3}{1250}\)
b, B = \(\dfrac{3}{2.5}\)+ \(\dfrac{3}{5.8}\) + \(\dfrac{3}{8.11}\) + \(\dfrac{3}{11.14}\)
c, C = \(\dfrac{5}{2}\) + \(\dfrac{5}{6}\) + \(\dfrac{5}{12}\) + \(\dfrac{5}{20}\) + \(\dfrac{5}{30}\) + \(\dfrac{5}{42}\) + ........... + \(\dfrac{5}{110}\)
d, D = \(\dfrac{1}{2.3.4}\) + \(\dfrac{1}{3.4.5}\) + \(\dfrac{1}{4.5.6}\) + \(\dfrac{1}{5.6.7}\) + \(\dfrac{1}{6.7.8}\) + \(\dfrac{1}{7.8.9}\) + \(\dfrac{1}{8.9.10}\)
Bài 1 Tính
a) ( \(\dfrac{-2}{3}\) + \(1\dfrac{1}{4}\) - \(\dfrac{1}{6}\) ) : \(\dfrac{-24}{10}\)
b) \(\dfrac{13}{15}\) x 0.25 x 3 + ( \(\dfrac{8}{15}\) - \(1\dfrac{19}{60}\) ) \(1\dfrac{23}{24}\)
c) ( \(\dfrac{12}{32}\) + \(\dfrac{5}{-20}\) - \(\dfrac{10}{24}\) ) : \(\dfrac{2}{3}\)
d) \(4\dfrac{1}{2}\) : ( 2.5 - \(3\dfrac{3}{4}\) ) + ( -\(\dfrac{1}{2}\) )
e) \(\dfrac{-5}{2}\) : ( \(\dfrac{3}{4}\) - \(\dfrac{1}{2}\) )
A=\(\dfrac{2}{1.4}+\dfrac{2}{4.7}+\dfrac{2}{7.9}+...+\dfrac{2}{73.76}\)
Hãy tính A
A= 1+\(\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+........+\dfrac{1}{3^{2014}}\)
So sánh A với \(\dfrac{3}{2}\)