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Ta có: \(A=100^2+200^2+300^2+...+1000^2\)
\(=100^2\cdot\left(1+2^2+3^2+...+10^2\right)\)
\(=100^2\cdot385=3850000\)
S = 100^2+200^2+300^2+.....+1000^2
S=100^2+(100.2)^2+(100.3)^2+....+(100....
S = 100^2(1^2+2^2+3^2+...+10^2)
S=100^2.385
S=3850000
A=1002+2002+3002+...+10002=(100*1)2+(100*2)2+(100*3)2+...+(100*10)2
=1002*12+1002*22+...+1002*102
=1002(12+22+...+102)=10 000*385=3 850 000
\(A=100^2+200^2+300^2+...+1000^2\)
\(A=\left(100\cdot1\right)^2+\left(100\cdot2\right)^2+\left(100\cdot3\right)^2+...+\left(100\cdot10\right)^2\)
\(A=100^2\cdot1^2+100^2\cdot2^2+100^2\cdot3^2+...+100^2\cdot10^2\)
\(A=100^2\left(1^2+2^2+3^2+...+10^2\right)\)
\(A=10000\cdot385\)
\(A=3850000\)
Cách này có j sai các bạn bảo nhé
12+22+32+...+102=385
=>1+4+9+...+100=385
mà A=1002+2002+3002+...+10002
=10000+40000+90000+...+1000000
==>(10000+40000+90000+...+1000000) : (1+4+9+...+100)
=10000
==>A=10000 *385
A=3850000
A = 1002+ 2002+ 3002+ ... + 10002
A = 3850000
ĐS : 3850000
\(A=100^2+200^2+300^2+...+1000^2\)
\(A=100\left(1^2+2^2+3^2+...+10^2\right)\)
Mà \(1^2+2^2+3^2+...+10^2=385\)
\(A=100.385\)
\(A=38500\)
Nhận thấy :
1002 = 12.10000
2002 = 22.10000
....
10002 = 102.10000
=> 1002 + 2002 + ... + 10002 = (12 + 22 + ... + 102).10000 = 385.10000 = 3 850 000
Vậy A = 3 850 000
\(A=100^2+200^2+300^2+...+1000^2\)
=>\(A=100^2\left(1^2+2^2+3^2+...+10^2\right)\)
=>\(A=10000.385\)
=>\(A=3850000\)
\(A=100^2+200^2+300^2+......+1000^2\)
\(=1000^2\left(1^2+2^2+3^2+...+10^2\right)\)
\(=10000.385\\\)
\(=3850000\)
Có : A = 100^2.(1^2+2^2+3^2+....+12^2) = 10000 . 650 = 6500000
k mk nha
\(100^2+200^2+300^2+..+1200^2\)
=\(1^2\cdot100\cdot100+2^2\cdot100\cdot100+3^2\cdot100\cdot100+...+12^2\cdot100\cdot100\)
=\(100\cdot100\cdot\left(1^2+2^2+3^2+...+12^2\right)\)
=\(10000\cdot650=6500000\)
A = 1002 + 2002 + 3002 + ... + 10002
A = ( 1.100 )2 + ( 2 .100 )2 + ( 3. 100 )2 + ... + ( 10 . 100 )2
A = 1002 ( 12 + 22 + ... + 102 )
A = 1002 .385
A = 3850000
A = 1002 + 2002 + 3002 + ... + 10002
A = 1002 . (12 + 22 + 32 + ... + 102)
A = 10000 . 385
A = 3850000
\(A=100^2+200^2+300^2+...+1000^2\)
\(A=100^2\left(1+2^2+3^3+...+10^2\right)\)
\(A=10000.385\)
\(A=3850000\)
có \(1^2\cdot100^2=100^2\)
\(2^2\cdot100^2=200^2\)
\(3^2\cdot100^2=300^2\)
( từ đó tương tự)
\(\Rightarrow100^2+200^2+300^2+....+1000^2\)
\(=100^2\left(1^2+2^2+3^2+...+10^2\right)\)
mà đã có\(1^2+2^2+3^2+...+10^2=385\)
\(\Rightarrow100^2\cdot385==3850000\)
\(\Rightarrow100^2+200^2+300^2+....+1000^2=3850000\)
Ta có:
\(A=100^2+200^2+300^2+...+5000^2\)
\(\Rightarrow A=\left(1.100\right)^2+\left(2.100\right)^2+\left(3.100\right)^2+...+\left(50.100\right)^2\)
\(\Rightarrow A=1^2.100^2+2^2.100^2+3^2.100^2+...+50^2.100^2\)
\(\Rightarrow A=\left(1^2+2^2+3^2+...+50^2\right).100^2\)
\(\Rightarrow A=42925.100^2\)
\(\Rightarrow A=429250000\)
Vậy A = 429250000