Let an = number of odd digits in the base-10 expansion of 2n and let bn = total number of digits in 2n.
For eg, 28=256 and so a8=1 (5 is the only odd digit) and b8=3 (it is a 3 digit number).
Three problems:
A) Show that ∞∑n=1an2n=19
B) Show that S=∞∑n=1bn2n is an irrational number.
C) Show that S as defined in B) above satisfies S>11691023
[Solution]
For eg, 28=256 and so a8=1 (5 is the only odd digit) and b8=3 (it is a 3 digit number).
Three problems:
A) Show that ∞∑n=1an2n=19
B) Show that S=∞∑n=1bn2n is an irrational number.
C) Show that S as defined in B) above satisfies S>11691023
[Solution]