A = 1/1×2 + 1/2×3 + 1/3×4 + .. + 1/99×100
A = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/99 - 1/100
A = 1 - 1/100 < 1
\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)
\(A=1\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\right)\)
\(A=1-\frac{1}{100}< 1\)
=> ĐPCM
Ta có:
A = 1/1 x 2 + 1/2 x 3 + 1/3 x 4 + ..... + 1/99 x 100
A = 1- 1/2 + 1/2 - 1 /3 + 1/3 - 1/4 + ..... + 1/99 - 1/100
A = 1 - 1/100 < 1
nha bn
chúc bn học giỏi