One can use the tan addition formula to prove that? = 16 tan^-1(1/5) – 4 tan^-1(1/239). over three hundred years ago, the taylor series for tan-1(x) at x = 0 and this fact were combined to calculate the first 100 digits of a. estimate how many terms of the two series we should use to calculate those 100 digits. [2 marks] hint. the series for tan-1(239) converges much, much faster than that for tan-1(5). this means that to guarantee 100 digits of n using this approach, we should find an n such that the difference between 16 tan-1(1) and the nth partial sum for 16 tan-+() is less than about 10–102. you may use the fact that for a series satisfying the conditions of the alternating series test, the nth partial sum differs from the total sum by less than the absolute value of the (n + 1)th term. you may also use mathematica to pin down a suitable value of n.