Question

[My Dream]

Cho:

S=1-(1/2)+(1/3)-(1/4)+...+(1/2011)-(1/2012)+(1/2013)

P=(1/1007)+(1/1008)+...+(1/2013)

Tính (S-P)^2013

*Giúp mình nhé!! Giải chi tiết luôn nhé (chứ làm tắt mình ko hiểu)!! Mình tick cho!!*

Answer 1

[o0o nhật kiếm o0o]

Ta có : 

\(S=\left(1+\frac{1}{3}+..+\frac{1}{2011}+\frac{1}{2013}\right)-\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{2012}\right)\)

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

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

\(=\frac{1}{1007}+\frac{1}{1008}+...+\frac{1}{2013}=P\)

\(\Rightarrow\left(s-p\right)^{2013}=0^{2013}=0\)

Answer 2

[My Dream]

Thanks bạn nhiều nhé!! Tặng bạn 1 tk :>