=(100+121+144):(169+196)

=365:365

=1

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{2352}+\frac{1}{2450}\\ \)

\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{49.50}\)

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

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

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

`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`

S=2/3.7+2/7.1+2/11.15+...+2/95.99

S = \(\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{7}\right)+\frac{1}{2}.\left(\frac{1}{7}-\frac{1}{11}\right)+\frac{1}{2}.\left(\frac{1}{11}-\frac{1}{15}\right)+...+\frac{1}{2}.\left(\frac{1}{95}-\frac{1}{99}\right)\)

S = \(\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+...+\frac{1}{95}-\frac{1}{99}\right)\)

S = \(\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{99}\right)\)

S = \(\frac{1}{2}.\frac{32}{99}\)

S = \(\frac{16}{99}\)

M=1/2+1/6+1/12+1/20+..+1/110

M = \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{10.11}\)

M = \(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{10}-\frac{1}{11}\)

M = \(1-\frac{1}{11}\)

M = \(\frac{10}{11}\)

\(S=\dfrac{1}{6}+\dfrac{1}{12}+...+\dfrac{1}{600}+\dfrac{1}{650}\)

\(=\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{24\cdot25}+\dfrac{1}{25\cdot26}\)

\(=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{24}-\dfrac{1}{25}+\dfrac{1}{25}-\dfrac{1}{26}\)

\(=\dfrac{1}{2}-\dfrac{1}{26}=\dfrac{13-1}{26}=\dfrac{12}{26}=\dfrac{6}{13}\)

nhanh giúp mik vs

#)Giải :

Ta có : \(\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+...+\frac{1}{20}>\frac{1}{20}+\frac{1}{20}+\frac{1}{20}+...+\frac{1}{20}=\frac{10}{20}=\frac{1}{2}< \frac{5}{6}\)(có 10 số \(\frac{1}{20}\))

\(\Rightarrow\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+...+\frac{1}{20}< \frac{5}{6}\)

Hay \(S< \frac{5}{6}\left(đpcm\right)\)

Ta có :S=1/11+1/12+1/13+...+1/20<1/10+1/10+1/10+...+1/10(20 số hạng 1/10)

=>S<1/10.20=1/2<5/6

ĐPCM

Ta có \(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}\)

\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)

\(=1-\frac{1}{6}\)

\(=\frac{5}{6}\)

lớp mấy vay

Ta thấy: \(\frac{1}{11}>\frac{1}{20}\)

\(\frac{1}{12}>\frac{1}{20}\)

\(\frac{1}{13}>\frac{1}{20}\)

................

\(\frac{1}{19}>\frac{1}{20}\)

=>\(\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+...+\frac{1}{19}+\frac{1}{20}>\frac{1}{20}+\frac{1}{20}+\frac{1}{20}+...+\frac{1}{20}+\frac{1}{20}\)

=>\(S>\frac{10}{20}\)

=>\(S>\frac{1}{2}\)(1)

Lại có: 

\(\frac{1}{11}<\frac{1}{10}\)

\(\frac{1}{12}<\frac{1}{10}\)

\(\frac{1}{13}<\frac{1}{10}\)

................

\(\frac{1}{20}<\frac{1}{10}\)

=>\(\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+...+\frac{1}{20}<\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+...+\frac{1}{10}\)

=>\(S<\frac{10}{10}\)

=>S<1 (2)

Từ (1) và (2)

=>1/2<S<1

=>ĐPCM

Ta có: 

1/20=1/20

1/19>1/20

1/18>1/20

.....

1/11>1/20

Suy ra 1/11+1/12+1/13+...+1/20>1/20*10=1/2. Vậy S>1/2.

Tương tự, ta có:

1/11=1/11

1/12<1/11

1/13<1/11

....

1/20<1/11

Suy ra 1/11+1/12+1/13+...+1/20<1/11*10=10/11<11/11=1. Vậy S < 1.

VẬY 1/2< S<1