Question

So sánh :1/(1x2) + 1/(2x3) + ....... +1/(59x60) với 1

Answer 1

1/1.2+1/2.3+1/3.4+...+1/59.60

=1-1/2+1/2-1/3+1/3-1/4+...+1/59-1/60

=1-1/60

=59/60

vì 1>59/60

=> 1>1/1.2+1/2.3+1/3.4+...+1/59.60

chúc bạn học tốt nha

Answer 2

\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{59.60}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{59}-\frac{1}{60}\)

\(=1-\frac{1}{60}=\frac{59}{60}\)

Answer 3

Đặt \(C=\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{59\times60}\)

          \(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{59}-\frac{1}{60}\)

          \(=1-\frac{1}{60}< 1\)

=> C < 1 (đpcm)

Answer 4

Ta có : 

\(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{59.60}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{59}-\frac{1}{60}\)

\(=1-\frac{1}{60}< 1\)

Answer 5

\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+...+\frac{1}{59\cdot60}\)

\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{59}-\frac{1}{60}\)

\(=\frac{1}{1}-\frac{1}{60}\)

\(=\frac{60}{60}-\frac{1}{60}\)

\(=\frac{59}{60}\)

Ta có : \(\frac{59}{60}< 1\)nên \(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+...+\frac{1}{59\cdot60}< 1\)