\(\left(1+\frac{1}{1.3}\right).....\left(1+\frac{1}{2013.2015}\right)=\frac{2^2}{1.3}.....\frac{2014^2}{2013.2015}=\)\(\frac{2.3.....2014}{1.2.....2013}.\frac{2.3.....2014}{3.4.....2015}=2014.\frac{2}{2015}=\frac{4028}{2015}\)
\(\left(1+\frac{1}{1.3}\right)\left(1+\frac{1}{2.4}\right)\left(1+\frac{1}{3.5}\right)\left(1+\frac{1}{4.6}\right)...\left(1+\frac{1}{2013.2015}\right)\)
Hãy tính giá trị biểu thức
Chứng tỏ :
a, A = \(\dfrac{1}{2.4}+\dfrac{1}{4.6}+...+\dfrac{1}{2022.2024}\) < \(\dfrac{1}{4}\)
b, B =\(\dfrac{1}{1.3}+\dfrac{1}{3.5}+...+\dfrac{1}{2013.2015}< \dfrac{1}{2}\)
c, C =\(\dfrac{1}{3^2}+\dfrac{1}{5^2}+\dfrac{1}{7^2}+...+\dfrac{1}{2013^2}< \dfrac{1}{4}\)
d, D =\(\dfrac{1}{2^2}+\dfrac{1}{4^2}+\dfrac{1}{6^2}+...+\dfrac{1}{2014^2}< \dfrac{1}{2}\)
1/1.3-1/2.4+1/3.5-1/4.6+...+1/97.99-1/98.100 = ?
chứng minh rằng:1/1.3 + 1/2.4 + 1/3.5 + 1/4.6 +....+ 1/97.99 + 1/98.100 < 3/4
tính C=1.3+2.4+3.5+4.6+.....+(n-1).(n+1)
H=(1+1/1.3)*(1+1/2.4)*(1+1/3.5)*(1+1/4.6)*(1+1/5.7)
Nhanh đúng mk tick
chứng minh rằng 1^1.3 + 1^2.4 + 1^3.5 + 1^4.6 +...+ 1^97.99+ 1^98.100 < 3^4
1.chứng minh rằng : s = 1/4+1/16+1/36+....+1/100<1/2
2.tính :s = 1.3 +2.4+3.5 +4.6+.....+2016.2018