a)Chứng minh rằng nếu:
\(\frac{x}{a+2b+c}\)=\(\frac{y}{2a+b-c}\)=\(\frac{z}{4a-4b+c}\) thì \(\frac{a}{x+2y+z}\)=\(\frac{b}{2x+y-z}\)=\(\frac{c}{4x-4y+z}\)
b) Chứng mình rằng: S= \(\frac{1}{5^2}\)-\(\frac{1}{5^4}\)+\(\frac{1}{5^6}\)-...+\(\frac{1}{5^{4n-2}}\)-\(\frac{1}{5^{4n}}\)+...+\(\frac{1}{5^{2010}}\)-\(\frac{1}{5^{2012}}\) < \(\frac{1}{26}\)
CHo A = 1 + 1/3 + 1/5 + 1/7 + ... + 1/2009 +1/2011 và B = 1/2 + 1/4 + 1/6 + ... + 1/2010 + 1/2012 . Hãy so sánh A-B với 1
chứng minh vs mọi số tự nhiên n khác 0 ta có
5/3*7+5/7*11+...+5/(4n-1)*(4n+3) = 5n/3*(4n+3)
chứng minh vs mọi số tự nhiên n, n lớn hơn 2 ta có
3/9*14+3/14*19+...+3/(5n-1)*(5n+4) <1/15
Tính:
A=\(\frac{7}{3}\).\(\frac{11}{16}\)+\(\frac{10}{3}\).\(\frac{7}{16}\)-\(\frac{7}{6}\).\(\frac{5}{8}\)
B=1+2-3-4+5+6-7-8+.....+2005+2006-2007-2008+2009+2010
C=(1-\(\frac{1}{4}\))(1-\(\frac{1}{9}\))(1-\(\frac{1}{16}\))......(1-\(\frac{1}{100000}\))
D=\(\frac{17\frac{3}{4}.\frac{17}{5}+3\frac{2}{5}.82\frac{1}{4}}{2.34-3.17}\)
E=\(\frac{\frac{2008}{2011}+\frac{2009}{2010}+\frac{2010}{2009}+\frac{2011}{2008}+\frac{2012}{503}}{\frac{1}{2011}+\frac{1}{2010}+\frac{1}{2009}+\frac{1}{2008}}\)
F=(2-\(\frac{2}{1.3}\))+(2-\(\frac{2}{3.5}\))+(2-\(\frac{2}{5.7}\))+.....+(2-\(\frac{2}{2009.2011}\))
1.Tính: A=3/5+3/5^4+3/5^7+...+3/5^100
2.Chứng minh rằng: 1/3+2/3^2+3/3^3+4/3^4+5/3^5+...+100/3^100<3/4
3. Tính: S=a+a^2+a^3+a^4+...a^2022
B=a-a^2+a^3-a^4+...-a^2022
giúp mk vs ak :3
8) \(\dfrac{17}{-26}.\left(\dfrac{1}{6}-\dfrac{5}{3}\right):\dfrac{17}{13}-\dfrac{20}{3}.\left(\dfrac{2}{5}-\dfrac{1}{4}\right)+\dfrac{2}{3}.\left(\dfrac{6}{5}-\dfrac{9}{2}\right)\)
a) 2x-1/11+2x-2/12+2x-3/13=2x+5/5+2x+6/4+2x+7/3
b) x-1/2016+x-2/2015+x-3/2014+x-4/2013+x-5/2012 -5=0
c) x+2017/2+x+2015/3+x+2013/4+x+2011/5+8=0
\(\dfrac{x+4}{2000}+\dfrac{x+3}{2001}=\dfrac{x+2}{2002}+\dfrac{x+1}{2003}\)
1/* Chứng minh rằng:
\(\dfrac{1}{1\times2}+\dfrac{1}{3\times4}+\dfrac{1}{5\times6}+...\dfrac{1}{49\times50}=\dfrac{1}{26}+\dfrac{1}{27}+\dfrac{1}{28}+..+\dfrac{1}{50}\)
2/* Cho:
A=\(\dfrac{1}{1\times2}+\dfrac{1}{3\times4}+\dfrac{1}{5\times6}+.....+\dfrac{1}{99\times100}\). Chứng minh rằng:\(\dfrac{7}{12}< A>\dfrac{5}{6}\)
Các bn giúp mk những bài này nha!
Chứng minh:
\(\dfrac{1}{6}< \dfrac{1}{5^2}+\dfrac{1}{6^2}+\dfrac{1}{7^2}+........+\dfrac{1}{100^2}< \dfrac{1}{4}\)
