What's the value of this infinite series?
>>9044060
1/81
0.015?
.01234567891
~0.01
>>9044092
this is correct
>>9044098
>>9044106
>>9044129
these are not, see me after class. this is my office.
>>9044387
May I use the gas chamber?
[math]\sum_{n=0}^{\infty}n^-10^n=\frac{1/}{81}/[math]
[math]\sum_{n=0}^{\infty}n^-10^n=\frac{1/}{81}[/math]
>>9044971
that is correct, good job
[math]
\sum\limits_{n=0}^\inftyn10^{-n}=\sum\limits_{n=0}^\infty\sum\limits_{k=0}^n10^{-n}\\
=\left(\sum\limits_{n=0}^\infty10^{-n}\right)^2\\
=\frac{1}{81}
[/math]
You are all wrong using LaTeX :
[math]
\sum_{n=2}^{+\infty}{\frac{n-1}{10^n}}=\frac{1}{81}=\sum_{n=0}^{+\infty}{\frac{n}{10^{n+1}}}
[/math] (wrong in the indices)
http://mathworld.wolfram.com/ChampernowneConstant.html
>>9044998
1*10^-1 = 0.1
?????????
>>9044060
Pic = .1111... + .01111... + 0.001111... + ... = 0.1111... * 0.1111... = 1/81
>>9046851
Yes.
You absolute retard, learn about what a^b means.
>>9044060
just note that if we mark the sum as X
then 10X - x = 0.111111... = 1/9
so 9X = 1/9
so X = 1/81
>>9044060
This is the same thing as 1/90 + 1/900 + 1/9000 ...
So yeah 1/81