Find the interval of convergence of -x". Where p>0 is a fixed constant. The interval of convergence 'n² will depend on values of p. State those values.
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- Identify two subsequences of ((−1)^n + 1/n) which converge to different limits. You should include explicit formulas for the selector functions.Pick one of your two subsequences and write a proof of the fact that it converges.If x1, y1, are two positive unequal numbers and xn = (xn-1+ yn-1)/2 and yn= sqrt(xn-1yn-1) for all n>=2, Prove that the sequences <xn> and <yn> are monotonic and they converge to the same limit. *Prove each stepWhere it is converges?