Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(S=\frac{1}{11}+\frac{1}{12}+...+\frac{1}{20}\)
\(>\frac{1}{20}+\frac{1}{20}+...+\frac{1}{20}\)(10 số hạng)
\(=10.\frac{1}{20}=\frac{1}{2}\).
Vậy \(S>\frac{1}{2}\).
Ta có:\(\frac{1}{11}>\frac{1}{20};\frac{1}{12}>\frac{1}{20};\frac{1}{13}>\frac{1}{20};....;\frac{1}{19}>\frac{1}{20}\)
\(\Rightarrow\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+...+\frac{1}{20}>\frac{1}{20}+\frac{1}{20}+\frac{1}{20}+...+\frac{1}{20}\)(Có 10 phân số \(\frac{1}{20}\))
\(\Rightarrow\frac{1}{11}+\frac{1}{12}+...+\frac{1}{20}>\frac{10}{20}\)\(\Leftrightarrow S>\frac{10}{20}\)
Mà \(\frac{10}{20}=\frac{1}{2}\)nên
\(\Rightarrow S>\frac{1}{2}\)
ta thấy: 1/11;1/12;1/13;...;1/19;1/20 đều >1/20
=>1/11+1/12+...1/19+1/20>1/20+1/20...+1/20
1/11+1/12+...1/19+1/20>10/20
1/11+1/12+...1/19+1/20>1/2 vậy S>1/2
Ta thấy mỗi số hạng của tổng đều bé hơn 1/10
=>S<\(\frac{1}{10}.10=1\)
=>S<1
S = 1/11 + 1/12 + 1/13 + 1/14 + 1/15 + 1/16 + 1/17 + 1/18 + 1/19 + 1/20
S < 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10
S < 10 × 1/10
S < 1
1+2+3+4+5+6+7+8+9+10=55
11+12+13+14+15+16+17+18+19+20=155
1+2+3+4+5+6+7+8+9+10+11+12+13+14 +15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30-50-53=362
có \(\frac{1}{20}\) bé nhất suy ra
"có 10 số hạng "\(\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}+......+\frac{1}{20}>\frac{1}{20}.10\)
\(VT>\frac{10}{20}=\frac{1}{2}\)
vì 1/11>1/20
1/12>1/20...
1/13>1/20
nên 1/11+1/12+,,,,+1/20>1/20+1/20+,,,,+1/20=10/20=1/2(rút gọn
10 số 1/20
vậy S>1/2
A = - 1 + 3 - 5 + 7 - 9 + 11 - 13 + 15 - 17
A = (-1 + 11) + (3 - 13) + (7- 17) + (-5 + 15) - 9
= - 10 + 10 - 10 + 10 - 9
= (-10 + 10) + (-10 + 10) - 9
= 0 + 0 - 9
= - 9
B = 1+2-3-4+5+6-7-8+9+10-11-12+13+14-15-16+17+18-19-20
B =(1+2-3-4)+(5+6-7-8)+(9+10-11-12)+(13+14-15-16)+(17+18-19-20)
B = -4+ (-4) + (-4) + (-4) + (-4)
B = -4 x 5
B = -20
\(\frac{1}{11}\)> \(\frac{1}{20}\)
\(\frac{1}{12}\)> \(\frac{1}{20}\)
.
.
.
\(\frac{1}{19}\)>\(\frac{1}{20}\)
\(\frac{1}{20}\)= \(\frac{1}{20}\)
=> S = 1/11+1/12+...+1/20>1/20+1/20+1/20+1/20+1/20+1/20+1/20+1/20+1/20+1/20=10*1/20=1/2 (đpcm)
Ta có:
\(\frac{1}{11}>\frac{1}{20}\)
\(\frac{1}{12}>\frac{1}{20}\)
.............
\(\frac{1}{20}=\frac{1}{20}\)
\(\Rightarrow\frac{1}{11}+\frac{1}{12}+...+\frac{1}{20}>\frac{1}{20}+\frac{1}{20}+...+\frac{1}{20}\) ( 10 phân số \(\frac{1}{20}\))
\(\Leftrightarrow\frac{10.1}{20}=\frac{10}{20}=\frac{1}{2}\)
Vì \(\frac{1}{20}+\frac{1}{20}+...+\frac{1}{20}=\frac{1}{2}\). Mà \(\frac{1}{11}+\frac{1}{12}+...+\frac{1}{20}>\frac{1}{20}\Rightarrow\frac{1}{11}+\frac{1}{12}+...+\frac{1}{20}>\frac{1}{2}\)