Question

Chứng tỏ rằng : 

\(\frac{1}{1.2}\) + \(\frac{1}{2.3}\) + \(\frac{1}{3.4}\) +.....+\(\frac{1}{49.50}\) < 1

 

Answer 1

1/1.2+1/2.3+...+1/49.50

=1/1-1/50

=49/50 bé hơn 1 nên cái đó bé hơn 1

Answer 2

ta có : \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-...-\frac{1}{50}\)

\(=1-\frac{1}{50}=\frac{49}{50}\)

vì \(\frac{49}{50}<1\)

nên \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}<1\)