Question

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

va P=\(\frac{1}{1007}+\frac{1}{1008}+...+\frac{1}{2012}+\frac{1}{2013}\)

tinh (S-P)²⁰¹³

Answer 1

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

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

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

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

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

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

\(=P\)

\(\Leftrightarrow S-P=0\)

\(\Leftrightarrow\left(S-P\right)^{2013}=0\)

Answer 2

Cho mình hỏi sao lại trừ 2 lần (1/2 - 1/4 ....) thế ạ

Answer 3

Dạ thôi mình biết rồi ạ

Answer 4

tgdghfdhdg

vì cộng thêm1/2+1/4+...+1/2012 ở ngoặc thứ nhất

Answer 5

s=1-1/2013

s=2012/2013