Which term of the G.P.: `sqrt(2),1/(sqrt(2)),1/(2sqrt(2)),1/(4sqrt(2)), i s1/(512sqrt(2))?`

Find: the 10th term of the G.P. sqrt(2),1/(sqrt(2)),1/(2sqrt(2)),

(sqrt(3)+1+sqrt(3)+1)/(2sqrt(2))

log((sqrt2-1)/(sqrt2+1))

The matrix A={:[((1)/(sqrt(2)),(1)/(sqrt(2))),((-1)/(sqrt(2)),(-1)/(sqrt(2)))]:} is

Find the 5th term of the progression 1,((sqrt(2)-1))/(2sqrt(3)),\ ((3-2sqrt(2))/(12)),\ ((5sqrt(2)-7)/(24sqrt(3))),\ ddot

For all n in N, 1 + 1/(sqrt(2))+1/(sqrt(3))+1/(sqrt(4))++1/(sqrt(n))

Simplify each of the following : (i)(sqrt(2)+1)/(sqrt(2)-1)+(sqrt(2)-1)/(sqrt(2)+1)" "(ii)(sqrt(5)+sqrt(3))/(sqrt(5)-sqrt(3))+(sqrt(5)-sqrt(3))/(sqrt(5)+sqrt(3))" "(iii)(2)/(sqrt(5)+sqrt(3))+(1)/(sqrt(3)+sqrt(2))-(3)/(sqrt(5)+sqrt(2))" "(iv)(sqrt(7)+sqrt(5))/(sqrt(7)-sqrt(5))-(sqrt(7)-sqrt(5))/(sqrt(7)+sqrt(5))

Sum the series to infinity : sqrt(2)- (1)/(sqrt(2))+(1)/(2(sqrt(2)))-(1)/(4sqrt(2))+ ....

Suppose a ,b, and c are in A.P. and a^2, b^2 and c^2 are in G.P. If a

Simplify : (1)/(sqrt(3)+sqrt(2))-(1)/(sqrt(3)-sqrt(2))+(2)/(sqrt(2)+1)