" Find the value of "n," if "(1)/(sqrt(4x+1)){((1+sqrt(4x+1))/(2))^(n)-((1-sqrt(4x+1))/(2))^(n)}=a_(0)+a_(1)x+...+a_(5)x^(5)

(1)/(sqrt(4x+1)){((1+sqrt(sqrt(x+1)))/(2))^(n)-((1-sqrt(4x+1))/(2))^(n)}=a_(0)+a_(1)x

If 1/(sqrt(4x+1)){((1+sqrt(4x+1))/2)^n-((1-sqrt(4x+1))/2)^n}=a_0+a_1x then find the possible value of ndot

If 1/(sqrt(4x+1)){((1+sqrt(4x+1))/2)^n-((1-sqrt(4x+1))/2)^n}=a_0+a_1x then find the possible value of ndot

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 :

The Sequence {a_(n)}_(n=1)^(+oo) is defined by a_(1)=0 and a_(n+1)=a_(n)+4n+3,n>=1 . Find the value of lim_(n rarr+oo)(sqrt(a_(n))+sqrt(a_(4n))+sqrt(a_(4^(2)n))+sqrt(a_(4^(3)n))+......+sqrt(a_(4^(10)n)))/(sqrt(a_(n))+sqrt(a_(2n))+sqrt(a_(2^(2)n))+sqrt(a_(2^(3)n))+.....+sqrt(a_(2^(10)n)))

If a_(1) ge 0 for all t and a_(1), a_(2), a_(3),….,a_(n) are in A.P. then show that, (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)))