Consider the series ∑n=0∞54n. The sum of a series is defined as the limit of the sequence of partial sums, which means

(a) The n-th partial sum of the infinite series,

is

Multiplying both sides by 1/4 gives

Subtract this from and solve for :

(your solution is also correct)

(b) The infinite sum is equal to the limit of the n-th partial sum:

and the sum indeed converges to 20/3.

answer: 45

30 miles

step-by-step explanation:

we know that 60 seconds equals 1 minute and 60 minutes 1 hour

44 ft       60 sec     60 min     158400   ft

  *   *   =

1 sec       1 min       1 hour         hour

we know that there are 5280 ft per mile

158400   ft       1 mile         30 miles

  *   =

1   hour               5280 ft     1 hour

so in 1 hour   it can travel 30 miles