Question 1022931
a)  {{{S[n] = 20+20+20}}}+...+20+20 = 20n <--- twenty n's here
(The hare runs 20 meters at every minute.)


b) {{{S[n] = 1000+500+250}}}+125+...+{{{1000*0.5^(n-1)}}}
The sum for the first n terms of a geometric sequence is {{{S[n] = 1000*((1-0.5^n)/(1-0.5)) = 2000(1-0.5^n)}}}

c)The tortoise will arrive at the finish line after 100 minutes.  (20n = 2000 ==> n=100 minutes.)
At n=100 minutes, the hare would have traveled {{{2000(1-0.5^99)}}} meters, which is really close to 2000, but not quite the finish line yet, because there is still an infinitesimal distance remaining.