Real Analysis Answers

Using the principle of induction, prove that 64 is a factor of 3^(2n+2)- 8n-9 ∀ n∈N

Find the limit of the sequence section 3.2.6

Show that the series , ∞Σ n=1 (x/1+n^2x^2) is uniformly convergent in [ k,1] for any k>0.

Define partition

Does the sequence 3+ (-1)^n converge to 2. Justify

Prove that the sequence {an/n} is convergent where { an} is a bounded sequence

Suppose f(x)=x^2 -1 for x belongs to [-1,1] find the upper and lower darboux sum of

(i) four equally space interval

(ii) Ten equally space interval

(iii) n equally space interval

The function f(x)= sin^2x is uniformly continuous in the interval [0,π]. True or false