1/2x3+1/3x4+1/4x5+....

Mình chỉ bít thế thôi vì đầu bài ko rõ là bao nhiêu chữ số 0 ở 380......0

chỗ .....sau số 380 là điền dấu >.<.=

\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+......+\frac{1}{380}\)

=\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...............+\frac{1}{19.20}\)

=\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+..............+\frac{1}{19}-\frac{1}{20}\)

=\(\frac{1}{2}-\frac{1}{20}\)

=\(\frac{9}{20}\)

1/2.3 + 1/3.4 + 1/4.5 + ...... + 1/tự tính

1/2 - 1/3 + 1/3 - 1/4 + 1/4 -1/5 + .......+ 1/...-1 - 1/.....1

1/2 - 1/......1

\(N=\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{19\cdot20}\)

\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{19}-\dfrac{1}{20}=\dfrac{19}{20}\)

1920

\(\frac{1}{12}-\frac{1}{20}-...-\frac{1}{380}\)

\(=\frac{1}{3.4}-\frac{1}{4.5}-...-\frac{1}{19.20}\)

\(=\left(\frac{1}{3}-\frac{1}{4}\right)-\left(\frac{1}{4}-\frac{1}{5}\right)-\left(\frac{1}{5}-\frac{1}{6}\right)-...-\left(\frac{1}{19}-\frac{1}{20}\right)\)

\(=\frac{1}{3}-\frac{1}{4}-\frac{1}{4}+\frac{1}{5}-\frac{1}{5}+\frac{1}{6}-...-\frac{1}{19}+\frac{1}{20}\)

\(=\frac{1}{3}-\frac{1}{4}-\frac{1}{4}+\frac{1}{20}\)

\(=-\frac{7}{60}\)

`S=1/2 +1/6 +1/12 +1/20 +...+1/380`

`=1/(1.2)+1/(2.3) +1/(3.4)+1/(4.5)+...+1/(19.20)`

`=1-1/2 +1/2 -1/3 +1/3-1/4 +1/4 -1/5+....+1/19-1/20`

`=1-1/20=20/20 -1/20 =19/20`

1/2+1/6+1/12+1/20+...+1/380

=1/1.2+ 1/2.3+ 1/3.4+ 1/4.5+...+ 1/19.20

= 1/1-1/2+ 1/2-1/3+ 1/3-1/4+ 1/4-1/5+...+1/19-1/20

=1-1/29

=29/29-1/29

= 28/29

28/29