Question 1(1) Define what a monotone sequence is.[2](2) Show thatthe sequence sn=nn+1 ia an increasing sequence for all n.[5](3) Prove that a monotone increasing sequence is convergent if and only if it is bounded..[5](4) Prove that every convergent sequence is a cauchy sequence.[5](5) Test the convergence of the fiollowing series.(i)n=1n+1n(ii)n=1sin(1n)(6) Find the value of x when the series ??(n+1)nnn+1xn converge and diverge.(7) Does the series ??(-1)n-11n converge absolutely or not.[5]