Ta có:1/(3^n)+1/(3^(n+1))=2/(3^(n+1))
Áp dụng ta có:
1-1/3=2/3
1/3-1/(3^2)=2/(3^2)
1/(3^2)-1/(3^3)=2/(3^3)
....
1/(3^98)-1/(3^99)=2/(3^99).
Cộng từng vế các phép tính với nhau ta có:
1-1/(3^99)=2M.
Mà 1-1/(3^99)<1 nên 2M<1 nên M<1/2(đpcm)
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
Cho C = 1/3 + 1/3^2 + 1/3^2 + 1/3^3 + ... + 1/3^99
CMR C < 1/2
Bài 1 :Rút gọn A=2^100-2^99+2^97+...+2^2 -2
B=3^100-3^99+3^98-3^97+...+3^@ +1
bài 2:
Cho C =1/3+1/3^2+1/3^3+...=1/3^99
CMR C<1/2
cho C=1/3+1/3^2+1/3^3+...+1/3^99 CMR C<1/2
Cho C = 1/3 +(1/3)^2b + (1/3)^2 + (1/3)^3 + ... (1/3)^99
CMR C < 1/2
cho B= 1/2+ 1/22 +1/23+........+1/299. So sánh B với 1
cho C= 1/3+ ( 1/3)2+(1/3)2+..........+ (1/3)99. CMR C< 1/2
1.cho C= 1/3+1/32+1/33+1/34+......+1/399
cmr: C<1/2
