Gọi biểu thức trên là A
3A = 1 + 1/3 + 1/3^2 + … + 1/3^98`
3A – A = ( 1 + 1/3 + 1/3^2 + … + 1/3^98 ) – ( 1/3 + 1/3^2 + 1/3^3 + … + 1/3^99 )`
2A = 1 – 1/3^99
A = \(\dfrac{1-\dfrac{1}{3^{99}}}{2}\)
Chứng minh Q=1/3+1/3^2+1/3^3+....+1/3^99+1/3^100<1/2
1/ Cho A= \(\dfrac{1}{3}\)-\(\dfrac{2}{3^2}\)+\(\dfrac{3}{3^3}\)-\(\dfrac{4}{3^4}\)+.....+\(\dfrac{99}{3^{99}}\)-\(\dfrac{100}{3^{100}}\) Chứng minh A < \(\dfrac{3}{16}\)
2/ Cho B=(\(\dfrac{1}{2^2}\)-1)(\(\dfrac{1}{3^2}\)-1)....(\(\dfrac{1}{100^2}\)-1) So sánh B và \(\dfrac{-1}{2}\)
chứng minh rằng M=1/3+1/3^2+1/3^3+......+1/3^99 < 1/2
Chứng minh: 1/3+1/3^2+1/3^3+.......+1/3^99 <1/2
cho A: 1/3+1/3^2+1/3^3+...+1/3^99 chứng minh rằng A<1/2
cho C=1/3+1/3^2+1/3^3+...+1/3^99.Chứng minh rằng C<1/2
\(C=\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+...+\dfrac{1}{3^{99}}\)
chứng minh C <\(\dfrac{1}{2}\)
Cho C=1/3+1/3^2+1/3^3+................+1/3^99
Chứng minh: C < 1/2
Cho C =1/3 + 1/3^2 + 1/3^3 +...+ 1/3^99
Chứng minh: C < 1/2
