CMR : 1/5^2-1/5^4+1/5^6-1/5^8+.................+1/5^2014-1/5^2012 <1/26
1Tính nhanh
A=1-2-3+4+5+6-7+8+......+2011-2012-2013+2014
B=1+2-3-4+5-6-7-8+9+.....+2014-2015-2016+2017
(Nhớ giải chi tiết nhé!)
CHỨNG MINH 1/2-1/3+1/4-1/5+1/6-1/7+....+1/2012-1/2013+1/2014 < 2/5
chứng minh : 1/2 - 1/3 + 1/4 - 1/5 + 1/6 - 1/7+.............+ 1/2012 - 1/2013 + 1/2014 < 2/5 giải hộ mik
Chứng minh S=1/2-1/3+1/4-1/5+1/6-1/7+...+1/2012-1/2013+1/2014 <2/5
1.Tìm tất cả các số tự nhiên n thỏa mãn:
\(2.2^2+3.2^3+4.2^4+...+\left(n-1\right)^{2n -1}+n.2^n=8192\)
2. So sánh A và B biết:
\(A=\frac{2011}{1.2}+\frac{2011}{3.4}+\frac{2011}{5.6}+...+\frac{2011}{1999.2000}\)
\(B=\frac{2012}{1001}+\frac{2012}{1002}+\frac{2012}{1003}+...+\frac{2012}{2000}\)
3. Tính \(\left(S-P\right)^{2016}\) biết:\(S=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2013}-\frac{1}{2014}+\frac{1}{2015}\)
\(P=\frac{1}{1008}+\frac{1}{1009}+\frac{1}{1010}+...+\frac{1}{2014}+\frac{1}{2015}\)
4.Tìm x:
a) \(-1\frac{1}{56}:\left(\frac{1}{8}-\frac{1}{7}\right)-\frac{22}{\left|2.x-0,5\right|}=-1\frac{1}{30}:\left(\frac{1}{5}-\frac{1}{6}\right)\)
b) \(\frac{1}{4}.\frac{2}{6}.\frac{3}{8}.\frac{4}{10}.\frac{5}{12}....\frac{30}{62}.\frac{31}{64}=2^x\)
c) \(\frac{4^5+4^5+4^5+4^5}{3^5+3^5+3^5}.\frac{6^5+6^5+6^5+6^5+6^5+6^5}{2^5+2^5}=2^x\)
1+2-3-4+5+6-7-8+9+1-.........+2010-2011-2012+2013+2014-2015-2016+2017
A= 1+ 2- 3- 4+ 5+ 6- 7- 8+ 9+ ... -2012+ 2013+ 2014
A=1+2-3-4+5+6-7-8+9+...-2012+2013+2014
A=1+(2-3-4+5)+(6-7-8+9)+...+(2010-2011-2012+2013)+2014
A=1+0+0+...+0+2014
A=2015
1 + 2 - 3 - 4 + 5 + 6 - 7 - 8 + 9 + ... - 2012 + 2013 + 2014 ( có 2014 số, 2014 chia 4 dư 2)
= 1 + ( 2 - 3 - 4 + 5) + ( 6 - 7 - 8 + 9) + ... + ( 2010 - 2011 - 2012 + 2013) + 2014
= 1 + 0 + 0 + ... + 0 + 2014
= 2015 + 0 = 2015
A = 1 + 2 - 3 - 4 + 5 + 6 - 7 - 8 + 9 + ... - 2012 + 2013 + 2014
= 1 + 2014 + (2 - 3 - 4 + 5) + (6 - 7 - 8 + 9) + ... + (2010 - 2011 - 2012 + 2013) = 2015 + 0 + 0 + ... + 0 = 2015
(1/2012+1/2013-1/2014)/(5/2012+5/2013-5/2014)-(2/2103+2/2014-2/2015)/(3/2013+3/2014-3/2015)
\(\frac{\frac{1}{2012}+\frac{1}{2013}-\frac{1}{2014}}{\frac{5}{2012}+\frac{5}{2013}-\frac{5}{2014}}-\frac{\frac{2}{2013}+\frac{2}{2014}-\frac{2}{2015}}{\frac{3}{2013}+\frac{3}{2014}-\frac{3}{2015}}\)
=\(\frac{\frac{1}{2012}+\frac{1}{2013}-\frac{1}{2014}}{5\left(\frac{1}{2012}+\frac{1}{2013}-\frac{1}{2014}\right)}-\frac{2\left(\frac{1}{2013}+\frac{1}{2014}-\frac{1}{2015}\right)}{3\left(\frac{1}{2013}+\frac{1}{2014}-\frac{1}{2015}\right)}=\frac{1}{5}-\frac{2}{3}=\frac{3}{15}-\frac{10}{15}=-\frac{7}{15}\)
A=1+2-3-4+5+6-7-8-...-2012+2013+2014-2015-2016