\(\frac{1}{1.2.3.4}+\frac{1}{2.3.4.5}+...+\frac{1}{27.28.29.30}\)
\(=\frac{1}{3}\left(\frac{3}{1.2.3.4}+\frac{3}{2.3.4.5}+...+\frac{3}{27.28.29.30}\right)\)
\(=\frac{1}{3}\left(\frac{1}{1.2.3}-\frac{1}{2.3.4}+\frac{1}{2.3.4}-\frac{1}{3.4.5}+...+\frac{1}{27.28.29}-\frac{1}{28.29.30}\right)\)
\(=\frac{1}{3}\left(\frac{1}{1.2.3}-\frac{1}{28.29.30}\right)\)
Tìm x: \(\frac{1}{1.2.3}+\frac{1}{2.3.4}+..+\frac{1}{98.99.100}-3x=\frac{1}{1.2.3.4}+\frac{1}{2.3.4.5}+..+\frac{1}{27.28.29.30}\)
Tìm x biết :
( \(\frac{1}{1.2.3.4}\)+ \(\frac{1}{2.3.4.5}\)+...+ \(\frac{1}{27.28.29.30}\)) x = -3
\(\text{Tính tổng: }\dfrac{1}{1.2.3.4}+\dfrac{1}{2.3.4.5}+\dfrac{1}{3.4.5.6}+...+\dfrac{1}{27.28.29.30}\)
Tính :
\(\frac{1}{1.2.3.4}+\frac{1}{2.3.4.5}+......+\frac{1}{17.18.19.20}\)
\(\frac{1}{1.2.3.4}+\frac{1}{2.3.4.5}+\frac{1}{3.4.5.6}+...+\frac{1}{200.201.202.203}\)
tính tổng trên
Tính tổng : A = \(\frac{1}{1.2.3.4}+\frac{1}{2.3.4.5}+\frac{1}{3.4.5.6}+...+\frac{1}{98.99.100.101}\)
\(c=\frac{1}{1.2.3.4}+\frac{1}{2.3.4.5}+\frac{1}{3.4.5.6}+...+\frac{1}{98.99.100.101}\)= ?
Tính :
\(A=\left(1-\frac{1}{1.2}\right)\left(1-\frac{1}{1.2.3}\right)\left(1-\frac{1}{1.2.3.4}\right)...\left(1-\frac{1}{1.2.3.4.....1986}\right)\)
CM:
1+\(\frac{1}{1.2}+\frac{1}{1.2.3}+\frac{1}{1.2.3.4}+...+\frac{1}{1.2.3...n}< 2\)
