A) 26+27+28+...+99+100
B) 2+4+6+...+98+100
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a) 57 + 26 +34 +63 = ( 57 + 63 ) + ( 26 + 34 )
= 120 + 60 = 180
b) 119 + 36 +201+184-37 = ( 119 + 201 ) + ( 36 +184 ) - 37
= 320 + 220 - 37
= 540 - 37 = 503
c) 24 + 25 +26+27+28+29+30+31 = ( 24 +31 ) + ( 25 + 30 ) + ( 26 +29) + ( 27 + 28 )
= 55 x 5 = 275
d) 2 + 4 + 6 + 8 +....+ 98+ 100
= {(100 + 2 ) x [(100 - 2) :2 + 1]} : 2
= 102 x 50 : 2
= 5100 : 2 = 2050
a) =180
b) = 503
c) = 220
d) mình không biết ý d
nhưng bạn k cho mình nha
\(A=\dfrac{101\cdot\dfrac{102}{2}}{\left(101-100\right)+99-98+...+3-2+1}\)
\(=\dfrac{101\cdot51}{1+1+...+1}=\dfrac{101\cdot51}{51}=101\)
\(B=\dfrac{37\cdot43\left(101-101\right)}{2+4+...+100}=0\)
a, \(A=\dfrac{101+100+99+98+...+3+2+1}{101-100+99-98+...+3-2+1}\)
Ta có: \(T=101+100+99+98+...+3+2+1\) \(=\dfrac{\left(101+1\right).101}{2}\)
\(=\dfrac{102.101}{2}\Leftrightarrow51.101\)
\(M=101-100+99-98+...+3-2+1\)
Ta có: \(101:2=50\) (dư \(1\))
\(\Rightarrow M=\left(101-100\right)+\left(99-98\right)+...+\left(3-2\right)+1\)
Có \(50\) dấu ngoặc tròn "\(\left(\right)\)"
\(\Rightarrow M=1+1+...+1+1=51.1=51\)
\(M\) có \(51\) số \(1\)
\(\Rightarrow A=\dfrac{T}{M}=\dfrac{51.101}{51}=101\)
Vậy \(A=101\)
b, \(B=\dfrac{3737.43-4343.37}{2+4+6+...100}\)
Ta có: \(T=3737.43-4343.37\)
\(T=37.101.43-43.101.37\)
\(T=0\)
\(\Rightarrow\) \(B=\dfrac{T}{2+4+6+...+100}=\dfrac{0}{2+4+6+...+100}\) \(=0\)
Vậy \(B=0\)
B=1+2-(3+4)+5+6-..-100+101
B=(3+11+19+...+195)-(7+15+...+199)+101
B=25.99-25.103+101
B=-100+101=1
Vậy B=1
\(A=\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{98.99.100}\)
\(A=\frac{1}{2}.\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{98.99.100}\right)\)
\(A=\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{98.99}-\frac{1}{99.100}\right)\)
\(A=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{9900}\right)\)
\(A=\frac{1}{2}.\frac{4949}{9900}\)
\(A=\frac{4949}{19800}\)
a)
C = 1 − 2 + 3 − 4 + ... + 97 − 98 + 99 − 100 = 1 − 2 + 3 − 4 + ... + 97 − 98 + 99 − 100 = − 1 + − 1 + ... + − 1 + − 1 = − 1.50 = − 50.
b)
B = 1 − 2 − 3 + 4 + 5 − 6 − 7 + ... + 97 − 98 − 99 + 100 = 1 − 2 + − 3 + 4 + 5 − 6 + ... + 97 − 98 + − 99 + 100 = − 1 + 1 + − 1 + ... + − 1 + 1 = − 1 + 1 + − 1 + 1 + ... + − 1 + 1 − 1 = 0 + 0 + ... + 0 − 1 = − 1.
Trả lời:
A= 26+27+28+...+99+100
A= (26+100)(100-26+1)/2=126x75/2=4725
Khoảng cách : `1`
Số hạng :
`(100-26)/1 + 1 = 75(số-hạng)`
Tổng :
`(100+26)xx75:2=4725`
_______________________________________
Khoảng cách : `2`
Số hạng :
`(100-2)/2 +1=50(số-hạng)`
Tổng :
`(100+2)xx50:2=2550`
_____________________________________
`#LeMichael`