(sqrt(2)h)/(8)+(sqrt(5)u)/(9)

(sqrt(24))/(8)+(sqrt(54))/(9)

Let U_(1)=1,U_(2)=1 and U_(n+2)=U_(n+1)+U_(n) for n>=1. Use mathematical induction to such that: :U_(n)=(1)/(sqrt(5)){((1+sqrt(5))/(2))^(n)-((1-sqrt(5))/(2))^(n)} for all n>1

Simplify: (i)\ ((sqrt(2))/5)^8\ -:((sqrt(2))/5)^(13)

(iii) ((sqrt(2))/(5))^(8)-:((sqrt(2))/(5))^(1/3)

(1)/(1+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(4))+(1)/(sqrt(4)+sqrt(5))+(1)/(sqrt(5)+sqrt(6))+(1)/(sqrt(6)+sqrt(7))+(1)/(sqrt(7)+sqrt(8))+(1)/(sqrt(8)+sqrt(9))

The value of (1)/(sqrt(4)+sqrt(5))+(1)/(sqrt(5)+sqrt(6))+(1)/(sqrt(6)+sqrt(7))+(1)/(sqrt(7)+sqrt(8))+(1)/(sqrt(8)+sqrt(9)) is

If U= [((1)/(sqrt2),(-1)/(sqrt2)),((1)/(sqrt2),(1)/(sqrt2))] , then U^(-1) is

The sum of the first n terms of the series 1/(sqrt(2) + sqrt(5)) + 1/(sqrt(5) + sqrt(8)) + 1/(sqrt(8) + sqrt(11)) +... is