Tính A = 1 + 3/2^3 + 4/2^4 + 5/2^5 + ... + 100/2^100
Những câu hỏi liên quan
Tính C=1/2-(1/3+2/3)+(1/4+2/4+3/4)-(1/5+2/5+3/5+4/5)+...+(1/100+2/100+...+99/100)
Tính:
A= 1+ 3/ 2^3 + 4/ 2^4 + 5/ 2^5 +..........+ 100/ 2^100
1.Tính: A=3/5+3/5^4+3/5^7+...+3/5^100
2.Chứng minh rằng: 1/3+2/3^2+3/3^3+4/3^4+5/3^5+...+100/3^100<3/4
3. Tính: S=a+a^2+a^3+a^4+...a^2022
B=a-a^2+a^3-a^4+...-a^2022
giúp mk vs ak :3
Bài 3:
a: a*S=a^2+a^3+...+a^2023
=>(a-1)*S=a^2023-a
=>\(S=\dfrac{a^{2023}-a}{a-1}\)
b: a*B=a^2-a^3+...-a^2023
=>(a+1)B=a-a^2023
=>\(B=\dfrac{a-a^{2023}}{a+1}\)
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Tính nhanh A = (1^100+2^100+…+10^100).(5^10-25^5)
B = (2^5+3^5+4^5).(1^2+2^2+…+100^2).(4^10-2^20)
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`Answer:`
\(A=\left(1^{100}+2^{100}+...+10^{100}\right)\left(5^{10}-25^5\right)\)
\(=\left(1^{100}+2^{100}+...+10^{100}\right)[5^{10}-\left(5^2\right)^5]\)
\(=\left(1^{100}+2^{100}+...+10^{100}\right)\left(5^{10}-5^{10}\right)\)
\(=\left(1^{100}+2^{100}+...+10^{100}\right).0\)
\(=0\)
\(B=\left(2^5+3^5+4^5\right)\left(1^2+2^2+...+100^2\right)\left(4^{10}-2^{20}\right)\)
\(=\left(2^5+3^5+4^5\right)\left(1^2+2^2+...+100^2\right)\left(2^{2.10}-2^{20}\right)\)
\(=\left(2^5+3^5+4^5\right)\left(1^2+2^2+...+100^2\right).0\)
\(=0\)
Tính A= 1+(3/2^3)+(4/2^4)+(5/2^5)+........+(100/2^100)
A=1+3/2^3+4/2^4+5/2^5+...100/2^100
1/2*A = 1/2 + 3/2^4 + 4/2^5 +....+ 99/2^100 + 100/2^101
A- A/2 = 1/2A =1/2 + 3/2^3 + 1/2^4 +...+1/2^100 - 100/2^101=
Tham khảo bài này nha
= [1/2+1/2^2 +1/2^3 +...+1/2^100] -100/2^101 (Do 3/2^3 = 1/2^2 +1/2^3)
=[1-(1/2)^101]/(1-1/2) -100/2^101 =
=(2^101 -1)/2^100 - 100/2^101
=> A= (2^101 -1)/2^99 - 100/2^100
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Tính A: 1+3/2^3+4/2^4+5/2^5+....+100/2^100
A=1+3/2^3+4/2^4+5/2^5+...100/2^100 tính A
tính A= 1+ 3/2^2+4/2^4+5/2^5+.....+100/2^100
A=1+3/2^3+4/2^4+5/2^5+...100/2^100
1/2*A = 1/2 + 3/2^4 + 4/2^5 +....+ 99/2^100 + 100/2^101
A- A/2 = 1/2A =1/2 + 3/2^3 + 1/2^4 +...+1/2^100 - 100/2^101=
= [1/2+1/2^2 +1/2^3 +...+1/2^100] -100/2^101 (Do 3/2^3 = 1/2^2 +1/2^3)
=[1-(1/2)^101]/(1-1/2) -100/2^101 =
=(2^101 -1)/2^100 - 100/2^101
=> A= (2^101 -1)/2^99 - 100/2^100
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tính nhanh
A=(1^100+2^100+…+10^100).(5^10-25^5)
B=(2^5+3^5+4^5).(1^2+2^2+…+100^2).(4^10-2^20)