![](https://rs.olm.vn/images/avt/0.png?1311)
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
B=1+2+(-3)+(-4)+5+6+(-7)+(-8)+...+2013+2014+(-2015)+(-2016)
B=(-4)+(-4)+...+(-4)
B=(-4).1008 (1008 vi co 1008 so (-4))
B=-4032
**** NHE
B = 1 + 2 + ( -3 ) + ( -4 ) + 5 + 6 + ( -7 ) + ( -8 ) +... + 2013 + 2014 + ( -2015 ) + ( -2016 )
B = 1 +[ 2 + ( -3 )] +[ ( -4 ) + 5] +[ 6 + ( -7 )] + [( -8 ) +9]+[10 +(-11)]+...+[(-2012)+2013]+ [2014 + ( -2015 ) ]+ ( -2016 )
B=[ 1 (-1) ] + [ 1 +( -1)] +[1 +(-1)] +...+[ 1 + (-1)] +(-2016)
B=0 + 0 0 +...+ 0 +(-2016)
B= -2016
![](https://rs.olm.vn/images/avt/0.png?1311)
1)
a) \(...=4^4-225=256-225=31\)
b) \(...=8.9.5+120=360-120=240\)
c) \(...=3^4-3^3=81-27=54\)
d) \(...=7^2-1=49-1=48\)
2) a) \(...=2^6=64\)
b) \(...=3^{15}:3^{10}=3^5=243\)
c) \(...=3^3-3^3=0\)
d) \(...=6^3+4^5=216+1024=1240\)
\(\frac{5}{1\cdot4}+\frac{5}{4\cdot7}+...+\frac{5}{2014\cdot2017}\)
\(=\frac{5}{3}\left(\frac{3}{1\cdot4}+\frac{3}{4\cdot7}+...+\frac{3}{2014\cdot2017}\right)\)
\(=\frac{5}{3}\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{2014}-\frac{1}{2017}\right)\)
\(=\frac{5}{3}\left(1-\frac{1}{2017}\right)\)
\(=\frac{5}{3}\cdot\frac{2016}{2017}=\frac{10080}{6051}=1\frac{4029}{6051}\)
\(S=\frac{5}{1.4}+\frac{5}{4.7}+...+\frac{5}{2014.2017}\)
\(S=5\left(\frac{1}{1.4}+\frac{1}{4.7}+...+\frac{1}{2014}-\frac{1}{2017}\right)\)
\(S=5.3\left(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{2014}-\frac{1}{2017}\right)\)
\(S=15.\left(\frac{1}{1}-\frac{1}{2017}\right)=15\cdot\frac{2016}{2017}=\frac{30240}{2017}\)