Chứng minh rằng:
a) A=1/3+1/(3^2)+1/(3^3)+...+1/(3^99)<1/2
b) B=3/(1^2*2^2)+5/(2^2*3^2)+7/(3^2*4^2)+...+19/(9^2*10^2)<1
c) C=1/3+2/(3^2)+3/(3^3)+4/(3^4)+...+100/(3^100)<3/4
a, 3-3/2.(2x-1)-1/2.(3x+2)=2x-3
b, 7/2+1/2.(4x-3/2)-1/3.(3-6x)=1/2.(x-1)
c, 3/2.(2x-1/2)-7/2.(3x+1/3)-1/2.(2x-1)=3x+5
Bài 1: Thực hiện phép tính.
A) 3: ( -1/2 )2 + 1/9 x Căn 36
B) 81 x ( 1/3)3 + 1/3
C) Căn 12 + Căn 27 - Căn 3
D) -32 - ( 1/2)-2 : 2 + (2/3)0 : (3/4)-1
E) 3/4 - ( -1/2 )2
F) 15/16 : (-2 2/3) + 15/16 : ( -1 3/5 )
G) 3/5 + -1/4 + 3/20
H) 3: ( -3/2)2 + 1/9 x căn 36
I) 272 x 85/ 66 x 323
J) (0.8)5/ (0.4)6
K) 272/ 242
L) (0.125)3 x 83
M) (-39)4 : 134
N) (0.6)5/ (0.2)6
O) ( 3/7 + 1/2 )2
P) 2:(1/2 - 2/3 )2
Q) 9x (-1/3)3 + 1/3
So sánh
a, 1/3 + 1/3^2 + 1/3^3 +....+ 1/3^99 + 1/3^100 và 1/2
b, 3/1^2*2^2 + 5/2^2 *3^2 +7/3^2*4^2 +......+ 19/9^2*10^2 và 1
so sánh
a)A=1/2^1+1/2^2+1/2^3+...+1/2^49+1/2^50 với 1
b)B=1/3^1 +1/3^2+1/3^3...+1/3^99+1/3^100 với 1/2
c)C=1/4^1+1/4^2+1/4^3+...+1/4^999+1/4^1000 với 1/3
Tính?
A = 3.\(\frac{1^3}{2}+6.\frac{1^2}{2}.\frac{-1^2}{3}+3.\frac{1}{2}.\frac{-1^3}{3}\)
B = \(3.\frac{1}{2}.\frac{-1}{3}\left(\frac{1^2}{2}+2.\frac{1}{2}.\frac{-1}{3}+\frac{-1^2}{3}\right)\)
a,Cho B = 1/2+1/2^2+1/2^3+...+1/2^99. So sánh B với 1
b, Cho C = 1/3+(1/3)^2+(1/3)^2+(1/3)^3+...+(1/3)^99. CMR C < 1/2
a) cho B = 1/2 + 1/2^2 + 1/2^3 +....+1/2^99. só sánh B với 1
b) cho C = 1/3 +(1/3)^2 + (1/3)^2 + (1/3)^3 + ..... + (1/3)^99. CMR C<1/2
a,Cho B = 1/2+1/2^2+1/2^3+...+1/2^99. So sánh B với 1
b, Cho C = 1/3+(1/3)^2+(1/3)^2+(1/3)^3+...+(1/3)^99. CMR C < 1/2
Bài 1: CMR 3/1^2*2^2 + 5/2^2*3^2 + 7/3^2*4^2 + ....... + 19/9^2*10^2 bé hơn 1
Bài 2: CMR 1/3 + 2/3^2 Bài 1: CMR 3/1^2*2^2 + 5/2^2*3^2 + 7/3^2*4^2 + ....... + 19/9^2*10^2 bé hơn 3/4
Bài 3: Cho A= 1/1*2 + 1/3*4 + 1/5*6 + .... + 1/99*100. CMR 7/12 < A < 5/6