\(2x-\dfrac{1}{2}-\dfrac{1}{6}-\dfrac{1}{12}-...-\dfrac{1}{49\cdot50}=7-\dfrac{1}{50}+x\)
\(\Leftrightarrow2x-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{49}-\dfrac{1}{50}\right)=x+\dfrac{349}{50}\)
\(\Leftrightarrow2x-\dfrac{49}{50}-x-\dfrac{349}{50}=0\)
=>x=398/50=199/25
2x-1/2-1/6-1/12-...-1/49.50=6-1/50+x
2x-1/2-1/16-1/12-....-1/49.50=7-1/50+x
CMR:
a) \(\frac{1}{1.2}+\frac{1}{3.4}+\frac{1}{5.6}+...+\frac{1}{49.50}=\frac{1}{26}+\frac{1}{27}+\frac{1}{28}+...+\frac{1}{50}\)
b) Cho A = \(\frac{1}{1.2}+\frac{1}{3.4}+\frac{1}{5.6}+...+\frac{1}{99.100}\)
CMR: \(\frac{7}{12}< A< \frac{5}{6}\)
CMR : \(\dfrac{1}{1.2}+\dfrac{1}{3.4}+...+\dfrac{1}{49.50}=\dfrac{1}{26}+\dfrac{1}{27}+...+\dfrac{1}{50}\)
Tìm các số hữu tỉ x trong các tỉ lệ thức:
a) 0,4: x=x:0,9
b) 0,2: hỗn số 1 và 1/5=2/3: (6x+7)
c) hỗn số 13 và 1/3: hỗn số 1 và 1/3=26: (2x+1)
d) x/3, 15=0, 15/7, 2
e) -2, 6/x=-12/42
f) x²/6=24/25
n) x-1/x+5=6/7
Help me
A=\(\dfrac{1}{1.2^2}+\dfrac{1}{2.3^2}+\dfrac{1}{3.4^2}+...+\dfrac{1}{49.50^2}\)
B=\(\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{50^2}\)
CM A<B
chứng minh rằng
\(\dfrac{1}{1.2}+\dfrac{1}{3.4}+\dfrac{1}{5.6}+...+\dfrac{1}{49.50}=\dfrac{1}{26}+\dfrac{1}{27}+...+\dfrac{1}{50}\)
CMR:
\(\dfrac{1}{1.2}+\dfrac{1}{3.4}+\dfrac{1}{5.6}+...+\dfrac{1}{49.50}=\dfrac{1}{26}+\dfrac{1}{27}+...+\dfrac{1}{50}\)
