(1/2-1).(1/3-1).(1/4-1).(1/5-1).......(1/2015-1)
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JS
26 tháng 3 2020
a. \(\left[\left(-2\right)^5.2014-4^2.2015\right]-\left(-2015^0+3^2-2^3\right)\)
\(=-64448-32240+1-9+8=-96688\)
27 tháng 3 2020
Tớ lm lại nhé:
SBC = 9-1/2-1/3-1/4-...-1/10
=1+1+...+1(9 số 1) -1/2-1/3-1/4-1/5-...-1/10.
=(1-1/2)+(1-1/3)+...+(1-1/10)
=1/2+2/3+...+9/10= SC
=> phép chia có thương là 1(vì SBC=SC)
27 tháng 6 2015
1/2-1/3+1/3-1/4+1/4-1/5+...+1/x-1/x+1=1/2015
1/2-1/x+1=1/2015
1/x+1=1/2-1/2015
1/x+1=2013/4030
2013/2013.(x+1)=2013/4030
2013.(x+1)=4030
x+1=4030:2013
x+1=4030/2013
x=4030/2013-1
x=2017/2013
BT
1
19 tháng 7 2018
\(\left(1+\frac{1}{1\cdot3}\right)\left(1+\frac{1}{2\cdot4}\right)\left(1+\frac{1}{3\cdot5}\right)\cdot...\cdot\left(1+\frac{1}{2015\cdot2017}\right)\cdot\frac{1}{2016}\)
\(=\frac{4}{3}\cdot\frac{9}{8}\cdot\frac{16}{15}\cdot...\cdot\frac{4064256}{4064255}\cdot\frac{1}{2016}\)
\(=\frac{\left(2\cdot2\right)\left(3\cdot3\right)\left(4\cdot4\right)\cdot...\cdot\left(2016\cdot2016\right)}{\left(1\cdot3\right)\left(2\cdot4\right)\left(3\cdot5\right)\cdot...\cdot\left(2015\cdot2017\right)}\cdot\frac{1}{2016}\)
\(=\frac{\left(2\cdot3\cdot4\cdot...\cdot2016\right)\left(2\cdot3\cdot4\cdot...\cdot2016\right)}{\left(1\cdot2\cdot3\cdot...\cdot2015\right)\left(3\cdot4\cdot5\cdot...\cdot2017\right)}\cdot\frac{1}{2016}\)
\(=\frac{2016\cdot2}{1\cdot2017}\cdot\frac{1}{2016}\)
\(=\frac{2}{2017}\)
WR
6 tháng 6 2015
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
6 tháng 6 2015
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