Kashmir University 3rd Semester Mathamatics guess check Here

Check your Guess below

Q.1Prove that Q the set of rational numbers is not complete ordered

field and R the set of real numbers is a complete ordered field.

Q2Prove that v8 is an irrational number.

Q.3 Show that the Union of countable sets is countable

Q.4 Show that subset of a countable set is countable

Q.5 Show that the set [0, 1] and R the set of real numbers

are uncountable sets. Q.6 show that every convergent sequence is bounded but not conversely.

Q.7 State and prove BOLZANO WEIERSTRASS Theorem

for sequence.

Q.8 The necessary and sufficient condition for the

sequence (an) be convergent is that Lim inf. (an}=Lim

super.(an)

Q.9 The Necessary and Sufficient condition for the convergence of a monotonic sequence is that it’s bounded.

Q.10 Prove that every Cauchy sequence is bounded but

not conversely.

Q.11 Prove the following

(1) lim3+2√(n+1)/√(n+1)=2

(ii) lim[v(n+1) -vn]=0

Q.12 State and prove Nested intervals Theorem Q.13 show that [1/n(n+1) is convergent and [n/(n+1

is not convergent.

Q.14 Prove that a positive term series [1/n^p is convergent iff p>1