A=5+5^2+5^3+5^4+...+5^100
LT
Những câu hỏi liên quan
A= 2^2 + 2^3 + 2^4 + 2^5 +...+ 2^100
B= 3^2 + 3^4 + 3^6 + ...+ 3^100
C=5^1 + 5^3 + 5^5 + ... + 5^99
Tính TỔNG QUÁT: S= a + a^2 + a^3 + a^4 + ...+ a^n
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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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)
A = 5/2*3*4 + 5/3*4*5 + ... + 5/98*99*100 + 5/99*100*101
Tính tổng A
Bài 1 : Chứng minh rằng :
a) 4/3 + 4/3^2 + 4/3^3 + ..... + 4/3^99 < 2
b) B = 1/5 + 2/5^2 + 3/5^3 + ..... + 100/5^100 < 5/16
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 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)
a) Cho P=5+5^2+5^3+5^4+5^5+...+5^102 .Chứng minh P:6 b) Cho A=1+4+4^2+4^3+...+4^100 Chứng minh A:5 c) Cho B = 1+2+2^2+2^3+...2^98 Chứng minh B:7 d) Cho C =1+3+3^2+3^3+...+3^104 Chứng minh C:40
Tính
a,1/5+1/5^2+1/5^3+1/5^4+...+1/100+1/4×5^100
bài 1
A=1*2*3+2*3*4+3*4*5+...+99*100*101
B=1*3*5+3*5*7+...+95*97*99
C=2*4+4*6+..+98*100
D=1*2+3*4+5*6+...+99*100
E=1^2+2^2+3^2+...+100^2
G=1*3+2*4+3*5+4*6+...+99*101+100*102
H=1*2^2+2*3^2+3*4^2+...+99*100^2
I=1*2*3+3*4*5+5*6*7+7*8*9+...+98*99*100
K=1^2+3^2+5^2+...+99^2
A = 1*2*3 + 2*3*4 + 3*4*5 ... + 99*100*101
=> 4A = 1*2*3*4 + 2*3*4*4 + 3*4*5*4 + ... +99*100*101*4
=> 4A = 1*2*3*4 + 2*3*4*(5 - 1) + 3*4*5*( 6 - 2) + ... + 99*100*101*(102 - 98)
=> 4A = 1*2*3*4 + 2*3*4*5 - 1*2*3*4 + 3*4*5*6 - 2*3*4*5 + ... + 99*100*101*102 - 98*99*100*101
=> 4A = 99*100*101*102
=> 4A = 101989800
=> A = 25497450