Đặt \(A=1.2.3+2.3.4+3.4.5+...+99.100.101\)
\(\Rightarrow4A=1.2.3.4+2.3.4.4+...+99.100.101.4\)
\(=1.2.3\left(4-0\right)+2.3.4\left(5-1\right)+...+99.100.101\left(102-98\right)\)
\(=\left(1.2.3.4+2.3.4.5+...+99.100+101.102\right)-\left(0.1.2.3+1.2.3.4+...+98.99.100.101\right)\)
\(=99.100.101.102-0.1.2.3\)
\(=101989800\)
\(\Rightarrow A=101989800:4=25497450\)
Vậy \(A=25497450.\)
p=1.2.3+2.3.4+3.4.5+...+99.100.101
A=1.2.3+2.3.4+3.4.5+...99.100.101.Tính A. Mơn nhiều ^_^
A= 1.2.3+2.3.4+3.4.5+..........+48.49.50
TÍnh A=\(\dfrac{1}{1.2}-\dfrac{1}{1.2.3}+\dfrac{1}{2.3}-\dfrac{1}{2.3.4}+\dfrac{1}{3.4}-\dfrac{1}{3.4.5}+...+\dfrac{1}{99.100}-\dfrac{1}{99.100.101}\)
B=\(\dfrac{5}{1.2.3.4}+\dfrac{5}{2.3.4.5}+...+\dfrac{5}{98.99.100.101}\)
C=\(\dfrac{6}{1^2+2^2}+\dfrac{10}{2^2+3^2}+\dfrac{14}{3^2+4^2}+...+\dfrac{398}{99^2.100^2}\)
So sanh s=2/1.2.3+2/2.3.4+2/3.4.5+...+2/2009.2010.2011 va p=1/2
Tính : \(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{48.49.50}\)
Tính giá trị của biểu thức:
M= 1/1.2.3+1/2.3.4+1/3.4.5+...+1/10.11.12
CMR: \(\frac{3}{1.2.3}+\frac{5}{2.3.4}+\frac{7}{3.4.5}+...+\frac{201}{100.101.102}< \frac{5}{4}\)
tính tổng :B=\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{37.38.39}\)
