Its given that the series are as follows:
∑ (arctan k)/(1 + kČ)
I did some searchings and readings about basic comparison test but i dont fully understand them.
Is the comparison between arctan k/1+kČ with Pi/4 and with (Pi/2)/(1/kČ) necessary?
Can i just compare in this manner?
0 < arctan k/ (1+kČ) < 2/kČ
I could not understand why that the numerator in the right equation has to be 2? can we use arctan k to replace the 2?
The factor is 2 because pi/2 is slightly inferior to 2. Actually, it's not a problem, we don't care about the constant factor. All we want to know is if we can compare the series with a Riemann series, which is the case, with a constant factor (not influencing the convergence) =)
arctan is always < pi/2