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\(A=11+14+17+...+62+65\)
Số số hạng của \(A\)là
\(\left(65-11\right)\div3+1=19\)(số hạng)
Tổng của \(A\)là:
\(\left(11+65\right)\times19\div2=722\)
Đáp số: 722
\(B=\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}\)
\(B=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}\)
\(B=\left(\frac{3-1}{1.3}+\frac{5-3}{3.5}+.....+\frac{9-7}{7.9}+\frac{11-9}{9.11}\right)\times\frac{1}{2}\)
\(B=\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+.....+\frac{1}{9}-\frac{1}{11}\right)\times\frac{1}{2}\)
\(B=\left(1-\frac{1}{11}\right)\times\frac{1}{2}\)
\(B=\frac{10}{11}\times\frac{1}{2}\)
\(B=\frac{5}{11}\)
\(C=\frac{3}{10}+\frac{3}{40}+\frac{3}{88}+\frac{3}{154}\)
\(C=\frac{3}{2.5}+\frac{3}{5.8}+\frac{3}{8.11}+\frac{3}{11.14}\)
\(C=\left(\frac{3}{2}-\frac{3}{5}+\frac{3}{5}-\frac{3}{8}+....+\frac{3}{11}-\frac{3}{14}\right)\div3\)
\(C=\left(\frac{3}{2}-\frac{3}{14}\right)\div3\)
\(C=\frac{9}{7}\div3\)
\(C=\frac{3}{7}\)
\(B=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}\)
\(B=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\)
\(B=1-\frac{1}{11}\)
\(B=\frac{10}{11}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
A = 3/1 + 3/1+2 + 3/1+2+3 + 3/1+2+3+4 + ...+3/1+2+..+100
A = 3/1 + 3/3 + 3/6 + 3/10 +..+3/5050
A = 2/2 .( 3/1 + 3/3 + 3/6 + 3/10 +...+ 3/5050)
A = 6/2 + 6/6 + 6/12 + 6/20 +..+6/10100)
A = 6 .(1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 +.. +1/100.101)
A = 6. (1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ...+1/100 - 1/101)
A = 6 (1 - 1/101)
A = 6 . 100/101
A = 600/101
![](https://rs.olm.vn/images/avt/0.png?1311)
A<10(1/40+1/50+1/70+1/60)=319/420<1
A>10(1/50+1/60+1/70+1/80)>7/12
=>7/12<A<1
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có:
7/12 = 4/12 + 3/12 = 1/3 + 1/4 = 20/60 + 20/80
1/41 + 1/42 + 1/43 +...+ 1/79 + 1/80 = (1/41 + 1/42 + 1/43 + ...+ 1/60) + (1/61 + 1/62 +...+ 1/79 + 1/80)
Do 1/41> 1/42 > 1/43 > ...>1/59 > 1/60
=> (1/41 + 1/42 + 1/43 + ...+ 1/60) > 1/60 + ...+ 1/60 = 20/60
và 1/61> 1/62> ... >1/79> 1/80
=> (1/61 + 1/62 +...+ 1/79 + 1/80) > 1/80 + ...+ 1/80 = 20/80
Vậy: 1/41 + 1/42 + 1/43 +...+ 1/79 + 1/80 > 20/60 + 20/80 = 7/12
=> 1/41 + 1/42 + 1/43 +...+ 1/79 + 1/80 > 7/12
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
thế thì cậu tự chứng minh đi làm sao cũng phải chứng minh toán học
\(A=\frac{1}{41}+\frac{1}{42}+...+\frac{1}{50}\)
Tổng trên có số số hạng là: \(\left(50-41\right)\div1+1=10\)(số hạng)
\(A=\frac{1}{41}+\frac{1}{42}+...+\frac{1}{50}< \frac{1}{40}+\frac{1}{40}+...+\frac{1}{40}=\frac{10}{40}=\frac{1}{4}\)