check if the sequence of digits after the decimal is non-terminating and non-periodic.
is 0.1010010010001........ a rational or irrational number?
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4 Answers
Hari Shankar
·2009-07-17 23:14:48
Samarth Kashyap
·2009-07-17 23:39:30
This is a problem frm I.A.Maron's book
0.1010010001......1000...(n times)1.... is irrational
To prove this, it is necessary to ascertain that the gicven decimal fraction is not a periodic one. there are n zeroes between nth and (n+1)th unities, whcih cannot occur in a periodic function.