Tính tổng:
A=\(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{99.101}\)
B=\(\frac{2}{4.7}+\frac{2}{7.10}+\frac{2}{10.13}+...+\frac{2}{100.103}\)
II) Tính nhanh:
a)\(\frac{3^2}{1.4}+\frac{3^2}{4.7}+\frac{3^2}{7.10}+...+\frac{3^2}{61.64}\)
b)\(\frac{1}{1.5}+\frac{1}{5.9}+\frac{1}{9.13}+...+\frac{1}{21.25}\)
c)\(\frac{2^2}{1.3}+\frac{3^2}{2.4}+\frac{4^2}{3.5}+...+\frac{20^2}{19.21}\)
nhanh choa tick * đg rất tức giận*
a) B = \(\frac{4}{1.3}+\frac{4}{3.5}+\frac{4}{5.7}+.......+\frac{4}{99.101}\)
b) C = \(\frac{5}{1.5}+\frac{5}{5.9}+\frac{5}{9.13}+......+\frac{5}{101.105}\)
bài 1 tính
A = \(\frac{2}{3.5}+\frac{2}{5.7}+..............+\frac{2}{37.39}\); B = \(\frac{4}{5.7}+\frac{4}{7.9}+..........+\frac{4}{59.61}\) ; C = \(\frac{4}{5.9}+\frac{4}{9.13}+.................+\frac{4}{41.45}\) Bài 2 chứng minh : \(\frac{m}{b.\left(b+m\right)}=\frac{1}{b}-\frac{1}{b+m}\)
Bài 1: Tính tổng sau :
A = \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)
B =\(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{99.101}\)
C =\(\frac{3^2}{10}+\frac{3^2}{40}+\frac{3^2}{88}+...+\frac{3^2}{340}\)
D =\(\frac{7}{1.3}+\frac{7}{3.5}+\frac{7}{5.7}+...+\frac{7}{99.101}\)
E =\(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^8}\)
G =\(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right).....\left(1-\frac{1}{99}\right)\)
Tìm x biết
a) \(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{47.49}=\frac{24}{x+1}\)
b) \(\frac{4}{1.5}+\frac{4}{5.9}+\frac{4}{9.13}+...+\frac{4}{97.101}=\frac{2x+4}{101}\)
c) \(\frac{x-1}{2017}+\frac{x-2}{2016}=\frac{x-3}{2015}+\frac{x-4}{2014}\)
d) \(\frac{x+1}{2017}+\frac{x+2}{2016}=\frac{x+3}{2015}+\frac{x+4}{2014}\)
Tính tổng:
a)\(\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+...+\frac{1}{24.25}\)
b)\(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{99.101}\)
Tính:
\(a,\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{110}+\frac{1}{132}\)
\(b,\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+....+\frac{2}{97.99}\)
Bài 1
a)\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\)\(\frac{1}{99.100}\) b)\(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{2015.2017}\)
c)\(\left(\frac{3}{2}+\frac{7}{6}+\frac{13}{12}+...+\frac{9901}{9900}\right)\)\(-\frac{99}{100}\) d)\(\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+...+\frac{3}{73.76}\)