Question

Challenge

Answer 1

converges :)

Answer 2

\[a_n={i*j*k\over10^n}\]
since i,k,j are are all single digits, as \(n\to\infty\), \(a_n\to0\)

Answer 3

and hence, the sum \(\displaystyle\sum a_n\) converges

Answer 4

hmmm what about qrst and uvwx

Answer 5

those are the random digits

Answer 6

between "0 and 1"
so, infact, the better thing to say is:
\[a_n=(100u+10v+w){1\over10^{3n}}\]

Answer 7

isnt it 0 to 9 instead of 0 and 1

Answer 8

yea... :)

Answer 9

ohk

Answer 10

nevertheless, does not change the system/..

Answer 11

thx.

Answer 12

yw.