Giải
Ta có A= [1+1/3.5] + [1+1/5.7] + [1+1/7.9] + ... + [1+1/37.39]
=>A= (1+1+1+...+1) +(1/3.5 + 1/5.7 + 1/7.9 + ... + 1/37.39)
=> A = 18 + 1/2.(2/3.5+2/5.7+2/7.9+...+2/37.39)
=>A = 18 + 1/2.(1/3-1/5+1/5-1/7+1/7-1/9+...+1/37-1/39)
=> A= 18 + 1/2.(1/3-1/39)
=> A= 18 + 1/2 . 4/13
=>A= 18 + 2/13 = 236/13
TÍNH A : \(\left[1+\frac{1}{3x5}\right]x\left[1+\frac{1}{5x7}\right]x.......x\left[1+\frac{1}{37x39}\right]\)
Bài tập tham khảo:
Bài 1: Tính tổng A = 1/3x5 + 1/5x7 + 1/7x9 + ......+1/37x39
\(\frac{1}{3x5}+\frac{1}{5x7}+\frac{1}{7x9}+...+\frac{1}{2009x2011}\)
1)\(\frac{4}{7}:\frac{-15}{28}x\left(-3\right)^2\) 2)\(\frac{15}{49}x1,4-\left(\frac{2}{3}+\frac{4}{5}\right);\frac{22}{10}\) 3)\(\frac{1}{4}-\frac{7}{4}:\left(-7\right)-3:\frac{3}{4}x\left(-2\right)^{^2}\)
4)\(\frac{5}{1x3}+\frac{5}{3x5}+\frac{5}{5x7}+....\frac{5}{197x199}\)
Tìm X :
a) \(\frac{2}{1x3}+\frac{2}{3x5}+\frac{2}{5x7}+...+\frac{2}{11x13}+x=\frac{24}{13}\)
b)\(1+\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x.\left(x+1\right)}=1\frac{2009}{2011}\)
Tính :
a) \(\left(1-\frac{1}{3}\right).\left(1-\frac{1}{6}\right).\left(1-\frac{1}{10}\right).\left(1-\frac{1}{15}\right).\left(1-\frac{1}{21}\right)...\left(1-\frac{1}{780}\right)\)
b) \(\left(1-\frac{1}{2}\right)+\left(1-\frac{1}{4}\right)+\left(1-\frac{1}{8}\right)+...+\left(1-\frac{1}{512}\right)+\left(1-\frac{1}{1024}\right)\)
Tính
a) \(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)...\left(1-\frac{1}{2018}\right)\)
b) \(\left(1-\frac{1}{3}\right)\left(1-\frac{1}{6}\right)\left(1-\frac{1}{10}\right)\left(1-\frac{1}{15}\right)...\left(1-\frac{1}{190}\right)\)
c) \(\left(1+\frac{7}{9}\right)\left(1+\frac{7}{20}\right)\left(1+\frac{7}{33}\right)\left(1+\frac{7}{48}\right)...\left(1+\frac{7}{2009}\right)\)
Tính
a) \(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)...\left(1-\frac{1}{2018}\right)\)
b) \(\left(1-\frac{1}{3}\right)\left(1-\frac{1}{6}\right)\left(1-\frac{1}{10}\right)\left(1-\frac{1}{15}\right)...\left(1-\frac{1}{190}\right)\)
c) \(\left(1+\frac{7}{9}\right)\left(1+\frac{7}{20}\right)\left(1+\frac{7}{33}\right)\left(1+\frac{7}{48}\right)...\left(1+\frac{7}{2009}\right)\)
Tính A = \(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{2014}\right)\left(1-\frac{1}{2015}\right)\left(1-\frac{1}{2016}\right)\)
