(1)/(sqrt(a_(1))+sqrt(a_(2)))+(1)/(sqrt(a_(2))+sqrt(a_(3)))+...+(1)/(sqrt(a_(n-1))+sqrt(a_(n)))=(n-1)/(sqrt(a_(1))+sqrt(a_(n)))

If a_(1), a_(2), a_(3),…..a_(n) are in A.P where a_(i) gt 0, AA I then (1)/(sqrt(a_(1)) + sqrt(a_(2))) + (1)/(sqrt(a_(2)) + sqrt(a_(3)))+ …+ (1)/(sqrt(a_(n-1)) + sqrt(a_(n))) = (k)/(sqrt(a_(1)) + sqrt(a_(n))) then k=

If a_(1),a_(2),a_(3)... are in A.P then prove that (1)/(sqrt(a)_(1)+sqrt(a)_(2))(+)/(sqrt(a)_(2)+sqrt(a)_(3))+...+(1)/(sqrt(a)_(n-1)+sqrt(a)_(n))=(n-1)/(sqrt(a)_(n)+sqrt(a)_(1))

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_(n) are in A.P then (sqrt(a_(1)) + sqrt(a_(n)))/( sqrt(a_(1)) + sqrt(a_(2))) + (sqrt(a_(1)) + sqrt(a_(n)))/(sqrt(a_(2)) + sqrt(a_(3))) + ….. + (sqrt( a_(1)) + sqrt(a_(n)))/( sqrt(a_(n - 1)) + sqrt(a_(n))) =

If a_(1),a_(2),...a_(n) are in AP,then (sqrt(a)_(1)+sqrt(a)_(n))/(sqrt(a)_(1)+sqrt(a)_(2))+(sqrt(a)_(1)+sqrt(a)_(n))/(sqrt(a)_(2)+sqrt(a)_(3))+...+(sqrt(a)_(1)+sqrt(a)_(n))/(sqrt(a)_(n-1)+sqrt(a)_(n))=

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_(1) , a_(2) , a_(3),"…………."a_(n) are in A.P., where a_(i) gt 0 for all i, then the value of : (1) /( sqrt(a_(1))+sqrt(a_(2)))+ (1) /( sqrt(a_(2))+sqrt(a_(3)))+"......"+(1) /( sqrt(a_(n-1))+sqrt(a_(n))) is :

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 :