Real Analysis Answers

Find

lim [1/(2n+1)^2

+2/(2n+2)^2+3/(2n+3)^2+..3/25n] n→ ∞

The function f(x)= [x]- x is not integrable in [ 0,3] , where [ x] denote greatest integer function.

True or false with full explanation

Prove that

lim 1/(x+5)^2 = ∞

x→-5

Prove that the union of a finite number of open sets is open

Test the series ∞ Σ n=1 (-1)^n-1. 3/(5n-2) for absolute and conditional convergence

The function f(x)= [x]- x is not integrable in [ 0,3] , where [ x] denote greatest integer function.

True or false with full explanation

Find

lim tan x sec^2 x- x/x^3

x→0

If f is monotonic on (a,b) then show that f is of bounded variation on(a,b)

{F} check,whether the collection G,given by:

G'={]1/n+2,1/n[:n€N}

is an open cover of ]0,1[