tính tổng: A = 1/10+ 1/15+1/21+...+1/120
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
A = 1/10 + 1/15 + 1/21 + ....+ 1/120
= 2/20 + 2/30 + 2/42 +....+ 2/240
= 2/4x5 + 2/5x6 + 2/6x7 + ...+ 2/15x16
= 2 x ( 1/4x5 + 1/5x6 + 1/6x7 +...+ 1/15x16)
=2 x ( 1/4 - 1/5 + 1/5 - 1/6 +1/6 - 1/7 + .....+ 1/15 - 1/16 )
= 2 x ( 1/4 - 1/16 )
= 2 x ( 4/16 - 1/16 )
= 2 x 3/16
= 6/16
= 3/8
tk nhé
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
A=\(2.\left(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+......+\frac{1}{240}\right)\)
A=\(2.\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+....+\frac{1}{15.16}\right)\)
A=\(2.\left(\frac{1}{4.}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+.......+\frac{1}{15}-\frac{1}{16}\right)\)
A=\(2.\left(\frac{1}{4}-\frac{1}{16}\right)\)
A=\(2.\left(\frac{4}{16}-\frac{1}{16}\right)\)
\(A=2.\frac{3}{16}\)
\(A=\frac{3}{8}\)
\(Vay\) \(A=\frac{3}{8}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
y = 1/10 + 1/15 + 1/21 + ... + 1/120
1/2y = 1/20 + 1/30 + 1/42 + ... + 1/240
1/2y = 1/4x5 + 1/5x6 + 1/6x7 + ... + 1/15x16
1/2y = 1/4 -1/5 + 1/5 - 1/6 + 1/6 -1/7 + ... +1/15 -1/16
1/2y = 1/4 - 1/16
1/2y = 3/16
y = 3/16 : 1/2
y = 3/16 x 2
y= 3/8
y=1/10 + 1/15 + 1/21 + ... + 1/120 (1)
Nhân cả 2 vế của đẳng thức (1) với 1/2 ta được:
1/2y=1/2.(1/10+1/15+1/21+...+1/120)
1/2y=1/20+1/30+1/42+...+1/240
1/2y=1/4.5+1/5.6+1/6.7+...+1/15.16
1/2y=1/4-1/5+1/5-1/6+1/6-1/7+...+1/15-1/16
1/2y=1/4-1/16
1/2y=4/16-1/16
1/2y=3/16
y=3/16:1/2
y=3/8
Vậy tổng dãy số trên bằng 3/8
Chúc bạn học tốt Nguyễn Minh Hiếu
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(C=\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+...+\frac{2}{240}=2\times\left(\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+...+\frac{1}{240}\right)\)
\(C=2\times\left(\frac{1}{4\times5}+\frac{1}{5\times6}+\frac{1}{6\times7}+...+\frac{1}{15\times16}\right)\)
\(C=2\times\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{15}-\frac{1}{16}\right)=2\times\left(\frac{1}{4}-\frac{1}{16}\right)=\frac{3}{8}\)
c = 2/20 + 2/30 +2/42 + ... 2 /240
=2/4.5 +2/5.6 + 2/6.7 + ... +1/15.16
=2. (1/4.5 + 1/5.6 + 1/6.7 +...+1/15.16)
= 2.(1/4-1/5+1/5-...-1/16)
=2.(1/4-1/6)=2.3/16=3/8.
ghi nho dau cham la dau nhan
![](https://rs.olm.vn/images/avt/0.png?1311)
\(S=\frac{2}{20}+\frac{2}{30}+...+\frac{2}{240}\)
\(=2\left(\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{15.16}\right)\)
\(=2\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{15}-\frac{1}{16}\right)\)
\(=2\left(\frac{1}{4}-\frac{1}{16}\right)\)
\(=2\times\frac{3}{16}\)
\(=\frac{3}{8}\)
Ta co: A = 1/10+ 1/15+1/21+...+1/120
= 2/20+2/30+2/42+...+2/240=2/(4*5)+2/(5*6)+.....+2/(15*16)
= 2*[1/(4*5)+1/(5*6)+...........+ 1/(15*16)]
= 2* [ 1/4-1/5+1/5-1/6+.........+1/15-1/16]
= 2*[1/4-1/16]
= 2*3/16
= 3/8
Vay A=3/8