For integer n≥0 , let In=∫π/40tann(x)dx. Rosel is helped by his friend Muhammad who suggested the known inequality 0≤tann(x)≤(4xπ)n, when x∈[0,π4]. Use this inequality to give a proof in the box below that Rosel remembers from the lectures of Dr Wordle that In
satisfies the reduction formula



I2n+1=12n−I2n−1,n≥1.



(i) Rosel calculates I1
and writes the answer as



I1=log AA.



Enter the value of A
in the box below:

A=

Preview .



(ii) By considering I2n+1
for increasing n
, starting with I1
, and assuming the limit (1) from (a), Rosel obtains the convergent series:



logA=1+a1+a2+a3+…



where a1,a2,a3,…
are real numbers. Specifically,



a1=

Incorrect
Your Answer: -1/4
Preview ,

a2=

Preview ,

a3=