Question 450317
{{{S[4] = 10&1/2 + 1/8 = 85/8}}}

{{{S[5] = 85/8 + 1/32 = 341/32}}}

The formula for the sum of an infinite geometric series is {{{S = s[1]/(1-r)}}}, where -1 < r <1.  Here r = 1/4.  Hence {{{S = 8/(1-1/4) = 8/(3/4) = 32/3}}}