1*2)^ -1+(2*3)^-1 + (3*4)^-1 +...+(2014*2015)^-1

1*2)^ -1+(2*3)^-1 + (3*4)^-1 +...+(2014*2015)^-1

1*2)^ -1+(2*3)^-1 + (3*4)^-1 +...+(2014*2015)^-1

ai tích mình mình tích lại

Ta có : 

\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{2004.2005}\)

\(=\)\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{2004}-\frac{1}{2005}\)

\(=\)\(\frac{1}{2}-\frac{1}{2005}\)

\(=\)\(\frac{2005}{4010}-\frac{2}{4010}\)

\(=\)\(\frac{2003}{4010}\)

Chúc bạn học tốt ~ 

Gọi \(A=\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{2014\cdot2015}\)

\(A=\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{2014\cdot2015}\)

\(A=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{2014}-\frac{1}{2015}\)

\(A=\frac{1}{2}-\frac{1}{2015}\)

\(A=\frac{2015}{4030}-\frac{2}{4030}\)

\(A=\frac{2013}{4030}\)

\(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{2014\cdot2015}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{2014}-\frac{1}{2015}\)

\(=\frac{1}{2}-\frac{1}{2015}\)Vì \(-\frac{1}{3}+\frac{1}{3}=0;-\frac{1}{4}+\frac{1}{4}=0;...\)

\(=\frac{2015}{4030}-\frac{2}{4030}\)

\(=\frac{2013}{4030}\)

=2015-(2015-2016)-2016+2^2017-2015-2²⁰¹⁵/2²⁰¹⁴-(1-4)-3-(5+6)+11

=(2015-2015)+(2016-2016)+2²-2+3-3-11+11

=0+0+(4-2)+(3-3)-(11-11)

=2

giải thích củ thể dùm mình cái

\(1.2.3....2015-1.2.3....2014-1.2.3....2013.2014^2\)

\(=1.2.3...\left(2014+1\right)-1.2.3...\left(2014+1\right)\)

\(=0\)

bạn làm thế là sai rồi 

có 3 con 2014 cơ mà 

bằng 15 hay sao ý

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

a) A = 1 + 2 + 4 + 8 + ... + 1024

=> A = 1 + (2 + 4 + 8 + ... + 1024)

                     có 512 số hạng

=> A = 1 + [(2 + 1024) . 512 : 2]

=> A = 1 + [1026 . 512 : 2]

=> A = 1 + 262656

=> A = 262657

-1 - 2 - 3 - 4 - .......... - 2015 - 2016 là số đối của 1 + 2 + 3 + 4 + .............. + 2015 + 2016

=> 1 + 2 + 3 + 4 + .............. + 2015 + 2016 = (2016 - 1 + 1) x ( 2016 + 1) : 2 = 2033136

mà 1 + 2 + 3 + 4 + ............... + 2015 + 2016 là số đối của -1 - 2 - 3 - 4 - ........ - 2015 - 2016

=> -1 - 2 - 3 - 4 - ............. - 2015 - 2016 = -2033136