A=1-(1-1/2)+1/3-(1/2-1/4)+..-(1/1006-1/2012)

A=1-1+1/2+1/3-1/2+1/4+...-1/1006+1/2012

A=(1-1)+(1/2-1/2)+...+(1/1006-1/1006)+1/1007+1/1008+..+1/2012

A=B => (A/B)^2013=1

Học tốt

B=\(\dfrac{1}{1007}+\dfrac{1}{1008}+...+\dfrac{1}{2012}+\dfrac{1}{2013}\)

=\(\left(1+\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{1006}+\dfrac{1}{1007}+...+\dfrac{1}{2012}+\dfrac{1}{2013}\right)\)- \(\left(1+\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{1006}\right)\)

=\(\left(1+\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{1006}+\dfrac{1}{1007}+...+\dfrac{1}{2012}+\dfrac{1}{2013}\right)\)-2\(\left(\dfrac{1}{2}+\dfrac{1}{4}+...+\dfrac{1}{2012}\right)\)

=1-\(\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{4}+...-\dfrac{1}{2012}+\dfrac{1}{2013}\)=S

( A-B)²⁰¹³ =0

Chúc ban học tốt nhé...!

A=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2013}-\frac{1}{2014}\)

tick đi mình giải cho

Ta có:\(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2011}-\frac{1}{2012}\)

=\(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2011}+\frac{1}{2012}-2.\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{2012}\right)\)

=\(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2012}-\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{1006}\right)\)

=\(\frac{1}{1007}+\frac{1}{1008}+...+\frac{1}{2012}\)

=>\(\left(\frac{A}{B}\right)^{2013}\)=(\(\frac{\frac{1}{1007}+\frac{1}{1008}+...+\frac{1}{2012}}{\frac{1}{1007}+\frac{1}{1008}+...+\frac{1}{2012}}^{ }\))²⁰¹³=1²⁰¹³=1

S = 1/3+1/5+1/7+...+1/2013-(1/2+1/4+1/6+...+1/2012)

S = 1/2+1/3+1/4+...+1/2012+1/2013 - 2(1/2+1/4+1/6+...+1/2012)

S = 1/2+1/3+1/4+...+1/2012+1/2013 - (1+1/2+1/3+...+1/1006)

S = 1/1007+1/1008+...+1/2013-1

=> S - P = 1/1007+1/1008+...+1/2013-1-(1/1007+1/1008+...+1/2013)

<=> S - P= -1 <=> (S-P)²⁰¹³ = -1

ket qua la (-1)