Answer to Question #85540 in Real Analysis for Tarun Bansal

Question

Are the following statements true or false?Give reasons for your answers and explain in details.
(a)Every subsequence of the sequence {1\n^(2)} is convergent
(b)The function f(x)=x^2+|x|,is differentiable at x=-1
(c)Every infinite set is an open set.
(d)A necessary condition for a function f to be integrable is that it is continuous.
(e)The sum of the series 3n∑r=1 1/3n+2r as n→∞ can be calculated by evaluating the integral ∫ 1/3+2x dx from 0 to 3.