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\(A=\left[1+\left(-2\right)\right]+\left[3+\left(-4\right)\right]+....+\left[2013+\left(-2014\right)+2015\right]\)
\(A=\left(-1\right)+\left(-1\right)+....+\left(-1\right)+2015\left(\text{1007 số hạng }\left(-1\right)\right)=1008\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Các số lẻ từ 1 đến 2015 có: (2015-1):2+1=1008 (số)
M=(1-3)+(5-7)+...+(2013-2015) có 504 cap unikey hong rui ban
M=(-2).504=-1008
Tick nhé
![](https://rs.olm.vn/images/avt/0.png?1311)
a/A=1+2+4+8+...+1024
2A=2+4+8+16+....+2048
2A-A=(2+4+8+16+....+2048)-(1+2+4+8+...+1024)
A=2048-1
A=2047
VẬY A=2047
b/B=1+5+25+125+....+15625
5B=5+25+125+625+....+78125
5B-B=(5+25+125+625+....+78125)-(1+5+25+125+....+15625)
4B=78125-1
4B=78124
B=78124:4
B=19531
VẬY B =19531
C=1/1.2+1/2.3+1/3.4+...+1/2015.2016
C=1-1/2+1/2-1/3+1/3-1/4+...+1/2015-1/2016
=1-1/2016
=2015/2016
VẬY C=2015/2016
D/=10/1.3+10/3.5+10/5.7+....+10/2013.2015
=5(2/1.3+2/3.5+2/5.7+...+2/2013.2015)
=5(1-1/3+1/3-1/5+1/5-1/7+..+1/2013-1/2015)
=5(1-1/2015)
=5.2014/2015
=2014/403
VẬY D=2014/403
a, A = 1 + 2 + 4 + 8 +...+ 1024
\(A=1+2+2^2+2^3+....+2^{10}\)
\(2A=2+2^2+2^3+....+2^{10}+2^{11}\)
\(A=1+2+2^2+2^3+....+2^{10}\)
\(A=2^{11}-1=2047\)
b, B = 1 + 5 + 25 + 125 + ... + 15625
\(B=1+5+5^2+5^3+....+5^6\)
\(3B=5+5^2+5^3+....+5^6+5^7\)
\(B=1+5+5^2+5^3+....+5^6\)
\(2B=5^7-1\Rightarrow B=\frac{5^7-1}{2}=39062\)
d, D = 10 / 1 . 3 + 10 / 3 . 5 + 10 / 5 . 7 + ... + 10 / 2013 . 2015
\(D=\frac{10}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{2013.2015}\right)\)
\(D=\frac{10}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+....+\frac{1}{2013}-\frac{1}{2015}\right)\)
\(D=\frac{10}{2}.\left(1-\frac{1}{2015}\right)=5.\frac{2014}{2015}=\frac{2014}{403}\)
Câu c thì tương tự
![](https://rs.olm.vn/images/avt/0.png?1311)
a, s1 có 2015 hạng tử
=> s1= (2014:2).-1+2015=1007.(-1)+2015=1008
Lời giải:
a,S1=1+(-2)+3+(-4)+...+(-2014)+2015
=(1-2)+(3-4)+...+(2013-2014)+2015
=-1+(-1)+...+(-1)+2015
=-1.1007+2015
=(-1007)+2015
=1008
b,S2=(-2)+4+(-6)+8+...+(-2014)+2016
=(-2+4)+(-6+8)+...+(-2014+2016)
=2+2+...+2
=2.504
=1008
c,S3=1+(-3)+5+(-7)+...+2013+(-2015)
=(1-3)+(5-7)+...+(2013-2015)
=(-2)+(-2)+...+(-2)
=(-2).504
=-1008
d,S4=(-2015)+(-2014)+(-2013)+...+2015+2016
=(-2015+2015)+...+0+2016
=0+...+0+2016
=2016
STUDY WELL !
![](https://rs.olm.vn/images/avt/0.png?1311)
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S=1-3+5-7+...-2015+2017
= (1-3)+(5-7)+......+(2013-2015)+2017
Số số hạng có từ 1 dến 2015 là: (2015-1):2+1=1008(số)
Vậy: Có 504 cặp số
Tổng= (-2).504+2017=1009
S = 1 - 3 + 5 - 7 + ... + 2009 - 2011 + 2013 - 2015 + 2017
SSH của S = ( 2017 - 1) : 2 + 1 = 1009 (Số hạng)
=> S = 1 - 3 + 5 - 7 + ... + 2009 - 2011 + 2013 - 2015 + 2017 (1009 số hạng)
= (1 - 3) + (5 - 7) + ... + (2009 - 2011) + (2013 - 2015) + 2017 (505 số hạng)
= (-2) + (-2) + ... + (-2) + (-2) + 2017 (505 số hạng)
=> (-2) . 504 + 2017
= (-1008) + 2017 = 1009
Vậy S = 1009
\(C=\frac{3}{3\cdot5}+\frac{3}{5\cdot7}+...+\frac{3}{2013\cdot2015}\) mới đúng nhé :">
Ta có: \(C=\frac{3}{3\cdot5}+\frac{3}{5\cdot7}+...+\frac{3}{2013\cdot2015}\)
\(\Rightarrow\frac{3}{2}C=\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+...+\frac{2}{2013\cdot2015}\)
\(\Rightarrow\frac{3}{2}C=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2013}-\frac{1}{2015}\)
\(\Rightarrow\frac{3}{2}C=\frac{1}{3}-\frac{1}{2015}=\frac{2015}{6045}-\frac{1}{6045}\)
\(\Rightarrow C=\frac{2014}{6045}:\frac{3}{2}=\frac{2014}{5045}\cdot\frac{2}{3}=\frac{4028}{15135}\)
\(C=\frac{3}{3.5}+\frac{3}{5.7}+\frac{3}{7.9}+...+\frac{3}{2013.2015}\)
\(=\frac{3}{2}\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{3013.2015}\right)\)
\(=\frac{3}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{2013}-\frac{1}{2015}\right)\)
\(=\frac{3}{2}\left(\frac{1}{3}-\frac{1}{2015}\right)\)
\(=\frac{3}{2}.\frac{2014}{6045}\)
\(=\frac{4028}{15135}\)
Study well ! >_<