\(\frac{3}{1.2}+\frac{3}{2.3}+........+\frac{3}{99.100}\)
\(=3\left(\frac{1}{1.2}+\frac{1}{2.3}+.....+\frac{1}{99.100}\right)\)
\(=3\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.........+\frac{1}{99}-\frac{1}{100}\right)\)
\(=3\left(1-\frac{1}{100}\right)\)
\(=\frac{3.99}{100}=\frac{297}{100}\)
b, B = 1\(\frac{1}{1x2}+\frac{1}{2x3}+......+\frac{1}{99x100}\)
c, C = \(\frac{1}{1x2}+\frac{1}{2x3}+......+\frac{1}{n\left(n+1\right)}\)
d, D = 1 + 2 + 3 + ......+ n
tinh tong S , biet : S = \(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+.......+\frac{1}{2010x2011}\)
k mk 3 cai nha mk k lai cho
tính:
a) \(\frac{1^2}{1x2}+\frac{2^2}{2x3}+\frac{3^2}{3x4}+...+\frac{100^2}{100x101}\)
b) \(\frac{2^2}{1x3}+\frac{3^2}{2x4}+\frac{4^2}{3x5}+...+\frac{59^2}{58x60}\)
\(\frac{1}{1x2}+\frac{1}{2x3}+.....+\frac{1}{99x100}\)
Tính ( Tính nhanh nếu có thể ) :
a , \(\frac{3}{40}+\frac{5}{3}+\frac{7}{60}\)
b , \(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+.....+\frac{1}{19x20}\)
Tính H=\(\frac{1}{1x2}\) -\(\frac{1}{1x2x3}\) +\(\frac{1}{2x3}\) -\(\frac{1}{2x3x4}\) +\(\frac{1}{3x4}\) -\(\frac{1}{3x4x5}\) +...+\(\frac{1}{99x100}\) -\(\frac{1}{99x100x101}\)
C=1x2+2x3+3x4+........+99x100
D=1x2x3+2x3x4+3x4x5+.......+98x99x100
E=12+22+52+.......+992
F=1/1x2+1/2x3+..........+1/99x100
G=1/1x2x3+1/2x3x4+........+1/99x98x100
H= 1/1x2x3x4+1/3x4x5x6+............+1/97x98x99x100
K= 1+1/2(1+2)+1/3(1+2+3)+........+1/30(1+2+30)
L=1/21+1/22+1/23+1/24+..............+1/210
M=2015/2015x2017-20162
\(\frac{ }{ }\)
Tính nhanh:
A= 1/2+1/2^2+1/2^3+....+1/2^100
B=3^2/2x4+3^2/4x6+3^2/6x8+....+3^2/198x200
C=\(\frac{\frac{2017}{1}+\frac{2017}{2}+\frac{2017}{3}+...+\frac{2017}{2017}}{\frac{2016}{1}+\frac{2015}{2}+\frac{2014}{3}+...+\frac{1}{2016}}\)
D=1x2+2x3+3x4+4x5+...+48x49
E=\(^{1^2+2^2+3^2+...+48^2}\)
F=1x49+2x48+3x47+...+48x2+49x1
Cho A = \(\frac{1}{1x2}+\frac{1}{3x4}+\frac{1}{4x5}+...+\frac{1}{99x100}\)
CM \(\frac{7}{12}\) < A < \(\frac{5}{6}\)
