Question

Tìm x biết:  -(1/3)-1/15-1/35-...-1/x.(x+2)=20/-21

Answer 1

-(1/3)-1/15-1/35-...-1/x.(x+2)=20/-21

=>1/3+1/15+1/35+...+1/x(x+2)=20/21

=>1/2 * (2/3 + 2/15 + 2/35 + ... + 2/x(x+2) )=20/21

=>\(\dfrac{2}{1\cdot3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{x\left(x+2\right)}=\dfrac{20}{21}:\dfrac{1}{2}\)

=>\(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{x}-\dfrac{1}{x+2}=\dfrac{40}{41}\)

=>\(1-\dfrac{1}{x+2}=\dfrac{40}{41}\)

=>\(\dfrac{1}{x+2}=1-\dfrac{40}{41}=\dfrac{1}{41}\)

=>x+2=41=>x=39

Answer 2

(1/3)-1/15-1/35-...-1/x.(x+2)=20/-21

=>1/3+1/15+1/35+...+1/x(x+2)=20/21

=>1/2 * (2/3 + 2/15 + 2/35 + ... + 2/x(x+2) )=20/21

=>1−13+13−15+15−17+...+1x−1x+2=40411−13+13−15+15−17+...+1x−1x+2=4041

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