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3) Since there are 12 months in a year, there are four groups of 3 months in a year.
So, if 420 dollars are saved every three months, a total of
dollars will be saved per year.
4) Using the given figure, the difference between the two numbers is composed by two little squares. If this difference is 72, then one little square is 36.
The sum of the two numbers is composed by 8 little squares, for a total of
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You've established that
so all you need to do is compute the integral. Rewrite the integrand as
and replace
, so that 
. Then
By the fundamental theorem of calculus, this evaluates to
and so the series converges.
You also could have used the fact that the series is geometric with common ratio less than 1 to arrive at the same conclusion, with the added perk of being able to find the exact value of the sum to corroborate this.
so all you need to do is compute the integral. Rewrite the integrand as
and replace
By the fundamental theorem of calculus, this evaluates to
and so the series converges.
You also could have used the fact that the series is geometric with common ratio less than 1 to arrive at the same conclusion, with the added perk of being able to find the exact value of the sum to corroborate this.