Question

Tìm X:

1/1 x 2 +1/2 x 3+ 1/3 x 4 + .........+1/ X x ( X +1) = 499/500

giải chi tiết gúp mình với ,cô sắp kểm tra rùi !!!!!!!!!!!!!!!

Answer 1

ta có:

1-1/2+1/2-1/3+1/3-1/4+....+1/x -1/x+1 =499/500

1-1/x+1 =499/500

1/x+1 =1/500 

x+1=500

x=499

Answer 2

\(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{X\times\left(X+1\right)}=\frac{499}{500}\)

\(\Leftrightarrow1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{X}-\frac{1}{X+1}=\frac{499}{500}\)

\(\Leftrightarrow1-\frac{1}{X+1}=\frac{499}{500}\)

\(\Leftrightarrow\frac{1}{X+1}=\frac{1}{500}\)

\(\Leftrightarrow X+1=500\)

\(\Leftrightarrow X=499\)

Answer 3

1x2 là mẫu à?