Question

1.Show that the sequence an defined by: a1= √ 2 & an+1=√ 2+an converges to 2:
2..Show that the sequence an defined by:a1=1 & an+1=√ 2+an , for all n>=1 converges to the positive root of the equation,X^2-X-2=0.
3. Using the definition show that ;lim n/2n-3 = ½ ii)lim 2n/n+1
n->∞ n-> ∞

4.determine whether the ff series is convergent or divergent by any appropriate test.
a) 1+ 2^p/2! +3^p/3! + 4^p/4! + …