Question

[Cá Bống]

Tìm x biết 1/1x2 + 1/2x3 + 1/3x4 + ... + 1/X(X+1) = 99/100

Answer 1

[Hồ Thu Giang]

\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.....+\frac{1}{x\left(x+1\right)}=\frac{99}{100}\)

\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+.....+\frac{1}{x}-\frac{1}{x+1}=\frac{99}{100}\)

\(1-\frac{1}{x+1}=\frac{99}{100}\)

=> \(\frac{1}{x+1}=1-\frac{99}{100}=\frac{1}{100}\)

=> x+1 = 100

=> x = 100 - 1 

=> x = 99

Answer 2

[KIM SEE YUN]

mơ đi Nguyễn Đình Dũng