Question

so sánh M = \(\frac{1}{1\times2}+\frac{1}{2\times3}+...+\frac{1}{49\times50}\) với 1

Answer 1

\(M=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+...+\frac{1}{49\cdot50}\)

\(M=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{49}-\frac{1}{50}\)

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

\(M=\frac{49}{50}\) < 1

VẬY M < 1 

Answer 2

M=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+............+\frac{1}{49}-\frac{1}{50}\)

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

Vậy M<1

Answer 3

M = 1/1.2 + 1/2.3 +...........+ 1/49.50

M = 1 - 1/2 + 1/2 -1 /3 +............+ 1/49 - 1/50

M = 1 - 1/50

M = 49/50 

Vì 49/50 < 1 => M < 1