Where can i practice some problems similar to this? (not necessarily programming problems ).
I really want to know how did most people solve this question? Did they use a software like WolframAlpha to solve the integral or did they really solve it.
Finally, I guess most people binary searched to find out the input.
From WolformAlpha I found answer for N=2, 3
so now a0=0, a1=2, a2=8/3, a3= 46/15
After some trail and guessing, I got the formula
aN = 2(1/1+1/3+1/5+…+1/(2*N-1)
I don’t know if it was a good experience.
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How to use these? As they just give the approx values in decimal. How you found the generalised result?
Same
What is wolformalpha??
What was your approach??
We can also use complex analysis: Find the residues at the poles of a contour integral, and in the limit, show that the contour integral equals the value of the given integral.
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Why did they gave non standard Calculus Problem in a Programming Contest ?
I did not studied any such theorems in my college 
.
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i did the same
If u subtract and manipulate the two consecutive values u will get the real fractions
like for N=2 the calculator gave 2.6667 , from here I guessed the fraction 0.6667 as 2/3 added 2 to get 8/3 and then for N=3 I got 3.06667 made it 30.6667 then did calculation and calculated the fraction as (1/10)*(30+2/3) and got 46/15 and for N=4 I got 3.35238 I subtracted this with N=3
i.e 3.06667 little cleverly and then i understood the pattern
Really great way of explanation. Thanks
glad you found it helpful!
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Can you clear how you used walformalpha
@codemaster7s
thanks for the feedback. I also included a link on my blog showing how you can do it on WolframAlpha. hope it helps!
We can find any integral in this??
@codemaster7s yea, pretty much. indefinite integrals are harder to calculate but if you specify range and have no unknown variables, it usually can give you a numerical answer. (perhaps they use numerical methods if the integration itself is nontrivial)