I have been thinking about a continuing decimal, i.e. 0.707007000700007...
obviously, the decimals composite parts are 0.7+0.007+0.000007+...
My question is this, is this decimal rational or irrational? And a reason why?
I first started thinking of geometrical progressions and summing to infinity, but I found that my common ratio, r, had to change to create the decimal, so I personally think it's irrational as the repeating block is changing?
i.e. 0.7 + 0.7(10^-2) + 0.7(10^-2)^2 + ... +
Does anyone have a neat proof of this or even better, think that I am wrong?
Kind regards, tom