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![](https://rs.olm.vn/images/avt/0.png?1311)
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
![](https://rs.olm.vn/images/avt/0.png?1311)
\(1+2+3+4+5+6+7+8+9+10=55\)
\(11+12+13+14+15+16+17+18+19+20=155\)
![](https://rs.olm.vn/images/avt/0.png?1311)
9+(-10)+11+(-12)+13+(-14)+15+(-16)
=[9+(-10)]+[11+(-12)]+[13+(-14)]+[15+(-16)]
=(-1)+(-1)+(-1)+(-1)
=(-1)x4
=-4
![](https://rs.olm.vn/images/avt/0.png?1311)
a) = 1/10 - 1/11 + 1/11 -1/12 + 1/12 - 1/13 +1/13 1/14 +...+ 1/78 - 1/79
= 1/10 - 1/79
= máy tính ok
mấy câu khác bn làm tương tự là đc nhưng nhớ nhanh thêm khoảng cách giữa các mẫu nha
a)\(\frac{1}{10.11}+\frac{1}{11.12}+...+\frac{1}{78.79}=\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+...+\frac{1}{78}-\frac{1}{79}=\frac{1}{10}-\frac{1}{79}=\frac{69}{790}\)
b) \(\frac{8}{7.9}+\frac{8}{9.11}+...+\frac{8}{133.135}=4\left(\frac{2}{7.9}+\frac{2}{9.11}+...+\frac{2}{133.135}\right)\)
\(=4\left(\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{133}-\frac{1}{135}\right)=4\left(\frac{1}{7}-\frac{1}{135}\right)=4.\frac{128}{945}=\frac{456}{945}\)
c) \(\frac{12}{8.11}+\frac{12}{11.14}+...+\frac{12}{503.506}=4\left(\frac{3}{8.11}+\frac{3}{11.14}+...+\frac{3}{503.506}\right)\)
\(=4\left(\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+...+\frac{1}{503}-\frac{1}{506}\right)=4\left(\frac{1}{8}-\frac{1}{506}\right)=\frac{249}{506}\)
d) \(\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{391.394}=\frac{1}{3}\left(\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{391.394}\right)\)
\(=\frac{1}{3}\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{391}-\frac{1}{394}\right)=\frac{1}{3}.\left(\frac{1}{4}-\frac{1}{394}\right)=\frac{1}{3}.\frac{195}{788}=\frac{65}{788}\)
e) \(\frac{4}{5.8}+\frac{4}{8.11}+...+\frac{4}{602.605}=\frac{4}{3}.\left(\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{602.605}\right)\)
\(=\frac{4}{3}\left(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{602}-\frac{1}{605}\right)=\frac{4}{3}\left(\frac{1}{5}-\frac{1}{605}\right)=\frac{4}{3}.\frac{24}{121}=\frac{32}{121}\)
g) Sửa đề\(1+\frac{1}{3}+\frac{1}{6}+...+\frac{1}{820}=2\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{1640}\right)=2\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{40.41}\right)\)
\(=2\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{40}-\frac{1}{41}\right)=2\left(1-\frac{1}{41}\right)=2.\frac{40}{41}=\frac{80}{41}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\text{A= 2+(-4)+(-6)+8+10+(-12)+(-14)+16+...+2010}\)
\(\text{A=[2+(-4)+(-6)+8] + [10+(-12)+(-14)+16] + ... + [2007+(-2008)+(-2009)+2010]}\)
\(\text{A= 0 + 0 + ... + 0}\)
\(\text{A= 0}\)
\(\text{B=1+(-3)+(-5)+7+9+(-11)+(-13)+15+...+2009}\)
\(\text{B=[1+(-3)+(-5)+7]+[9+(-11)+(-13)+15]+...+[2003+(-2005)+(-2007)+2009]}\)
\(\text{B=0 + 0 + ... + 0}\)
\(b=0\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a, Số các số hạng của dãy là :
( 175 - 1 ) : 2 + 1 = 88 ( số hạng )
Tổng dãy là :
( 175 + 1 ).88 : 2 = 7744
Đáp số : 7744
các câu sau tương tự nhé
Học tốt
a) \(1+3+5+7+...+173+175\)
\(\Rightarrow\frac{\left(175+1\right)\left[\left(175-1\right):2+1\right]}{2}=7744\)
b) \(6+8+10+12+...+170\)
\(\Rightarrow\frac{\left(170+6\right)\left[\left(170-1\right):2+1\right]}{2}=7524\)
c)\(2+5+8+11+...+200\)
\(\Rightarrow\frac{\left(200+2\right)\left[\left(200-2\right):3+1\right]}{2}=6767\)
d)\(4+7+10+13+...+400\)
\(\Rightarrow\frac{\left(400+4\right)\left[\left(400-4\right):3+1\right]}{2}=26866\)
e)\(1+5+9+...+401\)
\(\Rightarrow\frac{\left(401+1\right)\left[\left(401-1\right):4+1\right]}{2}=20301\)
g)\(1+6+11+16+...+566\)
\(\Rightarrow\frac{\left(566+1\right)\left[\left(566-1\right):5+1\right]}{2}=32319\)
=(-1)+(-1)+(-1)+(-1)
=-4
tk cho mk nha
9+(-10)+11+(-12)+13+(-14)+15+(-16)
=[9+(-10)]+[11+(-12)]+[15+(-16)]
= -1 +(-1) + (-1)
=-3