" If "a_(n+1)=sqrt((1)/(2)(1+a_(n)))" ,then "cos[(sqrt(1-a_(0)^(2)))/(a_(1)a_(2).....oo)]" is equal to "

if a_(r+1)=sqrt((1)/(2)(1+a_(r)), prove that )cos((sqrt(1-a_(0)^(2)))/(a_(1)*a_(2)*a_(3cdots*oo)))=a_(0)

If a_(1), a_(2), a_(3), a_(4) are in AP, then (1)/(sqrt(a_(1)) + sqrt(a_(2))) + (1)/(sqrt(a_(2)) + sqrt(a_(3))) + (1)/(sqrt(a_(3)) + sqrt(a_(4))) is equal to

If a_(r ) gt 0, r in N and a_(1), a_(2) , a_(3) ,"……..",a_(2n) are in A.P. then : (a_(1) + a_(2n))/( sqrt( a_(1))+ sqrt(a_(2))) + ( a_(2) + a_(2n-1))/(sqrt(a_(2)) + sqrt(a_(3)))+"......"(a_(n)+a_(n+1))/(sqrt(a_(n))+sqrt(a_(n+1))) is equal to :

Let a_(1),a_(2),a_(3),...,...,a_(49),a_(50) are in airthmetic progression. If a_(1)=4 and a_(50)=144 ,then the value of , (1)/(sqrt(a_(1))+sqrt(a_(2)))+(1)/(sqrt(a_(2))+sqrt(a_(3)))+(1)/(sqrt(a_(3))+sqrt(a_(4)))cdots+(1)/(sqrt(a_(49))+sqrt(a_(50))) is equal to

If a_(1),a_(2),a_(3),...,a_(2n+1) are in A.P.then (a_(2n+1)-a_(1))/(a_(2n+1)+a_(1))+(a_(2n)-a_(2))/(a_(2n)+a_(2))+...+(a_(n+2)-a_(n))/(a_(n+2)+a_(n)) is equal to (n(n+1))/(2)xx(a_(2)-a_(1))/(a_(n+1)) b.(n(n+1))/(2) c.(n+1)(a_(2)-a_(1)) d.none of these

If a_(1), a_(2), a_(3),….,a_(n) are in AP and a_(1) = 0 , then the value of ((a_(3))/(a_(2)) + (a_(4))/(a_(3)) +...+(a_(n))/a_(n-1))-a_(2) ((1)/(a_(2)) + (1)/(a_(3))+...+(1)/(a_(n-2))) is equal to a) (n-2) + (1)/((n-2)) b) (1)/((n-2)) c)(n - 2) d)(n - 1)

If a_(1),a_(2),...a_(n) are in H.P then the expression a_(1)a_(2)+a_(2)a_(3)+...+a_(n-1)a_(n) is equal to