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\(A=2+2^2+2^3+.....+2^{100}\)
\(2A=2.\left(2+2^2+2^3+.....+2^{100}\right)\)
\(2A=2^2+2^3+2^4+.........+2^{101}\)
\(2A-A=\left(2^2+2^3+2^4+....+2^{101}\right)-\left(2+2^2+2^3+....+2^{100}\right)\)
\(A=2^{101}-2\)
Ta có \(\frac{2^{100}.13+65.2^{100}}{2^{98}.104}\)
\(=\frac{2^{100}.\left(13+65\right)}{2^{98}.2.52}\)
\(=\frac{2^{100}.78}{2^{99}.52}\)
\(=\frac{2.78}{52}\)
\(=3\)
\(\frac{2^{100}.13+65.2^{100}}{2^{98}.104}=\frac{2^{100}.\left(13+65\right)}{2^{98}.104}\)
\(=\frac{2^{100}.78}{2^{98}.104}\) \(=\frac{2^2.78}{104}=\frac{4.78}{104}\)
\(=\frac{78}{26}=3\)
So so hang :
(100-1):1+1=100(so)
Tong:
100:2*(100+1)=5050
Ds 5050
so so hang:(100-1):1+1=100(so hang)
tong la:(100+1)*100:2=5050
ds:5050
\(E=1+5^2+5^4+...+5^{100}\)
\(\Rightarrow5^2E=25E=5^2+5^4+5^6+...+5^{102}\)
\(\Rightarrow25E-E=5^{102}-1\)
\(\Rightarrow E=\frac{5^{102}-1}{24}\)
A=100+98+96+...+2-97-95...-1
=(2+...+96+98+100)-(1+..+95+97)
={(100+2).[(100-2):2+1]:2}-{(97+1).[(97-1):2+1]:2}
=102.50:2-98.49:2
=(102.50-98.49):2
=(5100-4802):2
=298:2
=149
1+2-3-4+5+6-7-8+9+10-11-12+...+298-299-300+301+302
=1+(-5)+5+(-9)+9+(-13)+...+(-301)+301+302
=1+[(-5)+5]+[(-9)+9]+[(-13)+13]+...+[(-301)+301]+302
=1+0+0+0+...+0+302
=1+302
=303
Chúc bạn học giỏi nha!!1
A = 2 + 22 + 23 + .... + 2100.
2A=2(2 + 22 + 23 + .... + 2100.)
2A=22+23+...+2101
2A-A=(22+23+...+2101)-(2 + 22 + 23 + .... + 2100)
A=2101-2
a) 4,38 - 1,9 + 0,62 b) [(-100).(-1,6)]:(-2)
= (4,38 + 0,62) - 1,9 = 100.1,6 : (-2)
= 5 - 1,9 = 3,1 = 160 : (-2) = -80
c) (2,4.5,55): 1,11 d) 100. (2,01 + 3,99)
= 2,4. (5,55:1,11) = 100. 6
= 2,4. 5 =12 = 600