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![](https://rs.olm.vn/images/avt/0.png?1311)
\(A< \frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+....+\frac{1}{99.100}\)
\(A< \frac{1}{4}-\frac{1}{100}\)
\(A< \frac{6}{25}< \frac{1}{4}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Câu 2: a) 234-117+(-100)+(-234)=[234+(-234)]-117-100=0-117-100=-217
b) -927+1421+930+(-1421)=-927+930+[1421+(-1421)]=-927+930+0=3
Bài 1:
s1=1+(-3)+5+(-7)+............+17
s2=-2+4+(-6)+8+...........+(-18)
\(\Rightarrow\) s1 + s2 = (1-2-3+4)+(5-6-7+8)+...+(13-14-15+16)+17-18
= 0 + 0 + ...+ 0 + (-1)
= -1
Bài 2.
a) 234-117+(-100)+(-234)
= (-234 + 234 ) + [- 117 + (-100)]
= 0 + (-217)
= -217
b) -927+1421+930+(-1421)
= ( -1421 + 1421 ) + ( -927 + 930 )
= 0 + 3
= 3
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) Ta có:
S = 1 + 5 + 9 + 13 + ... + 2013 + 2017
S = (2017 + 1)[(2017 - 1) : 4 + 1] : 2
S = 2018.505 : 2
S = 1019090 ÷ 2
S = 509545
b) Ta có:
A = 1 + 3 + 32 + 33 + ... + 32016
3A = 3 + 32 + 33 + 34 + ... + 32017
3A - A = (3 + 32 + 33 + 34 + ... + 32017) - (1 + 3 + 32 + 33 + ... + 32016)
2A = 32017 - 1
A = \(\frac{3^{2017}-1}{2}\)
=> B - A = 32017 - \(\frac{3^{2017}-1}{2}\)
=> B - A = 32017 - \(\frac{3^{2017}}{2}-\frac{1}{2}\)
=> B - A = \(\frac{3^{2017}}{2}-0,5\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có : A = 1 + 3 + 32 + ....... + 32015
=> 3A = 3 + 32 + ....... + 32016
=> 3A - A = 32016 - 1
=> 2A = 32016 - 1
=> A = 32016 - 1/2
Mà B = 32016/2
=> B - A = 32016/2 - 32016 - 1/2
=> B - A = 1/2
Ta có: 3a-a=32016-1 <=> a=\(\frac{3^{2016}-1}{2}\)
=> b-a=\(\frac{3^{2016}}{2}-\frac{3^{2016}-1}{2}=\frac{1}{2}\)