Question

Câu 5:Biết rằng
Số trong đẳng thức trên bằng .

Answer 1

\(\frac{1}{x\left(x+1\right)}+\frac{1}{\left(x+1\right)\left(x+2\right)}+\frac{1}{\left(x+2\right)\left(x+3\right)}+...+\frac{1}{\left(x+99\right)\left(x+100\right)}=\frac{k}{x\left(x+100\right)}\)

\(\frac{1}{x}-\frac{1}{x+1}+\frac{1}{x+1}-\frac{1}{x+2}+\frac{1}{x+2}-\frac{1}{x+3}+...+\frac{1}{x+99}-\frac{1}{x+100}=\frac{k}{x\left(x+100\right)}\)

\(\frac{1}{x}-\frac{1}{x+100}=\frac{k}{x\left(x+100\right)}\)

\(\frac{x+100}{x\left(x+100\right)}-\frac{x}{x\left(x+100\right)}=\frac{k}{x\left(x+100\right)}\)

k = 100

Answer 2

k=100