The value of `lim_(ntooo)a_(n)` when `a_(n+1)=sqrt(2+a_(n)), n=1,2,3,`….. is

Solve lim_(n rarr oo)a_(n), when a_(n+1)=sqrt(2+a_(n)),n=1,2,3dots

If Lt_(ntooo)a_(n)=l" where "a_(n+1)=sqrt(2+a_(n)),n = 1,2,3...., find the value of l.

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)))

Prove that lim_(n rarr oo)a_(n)=-(1)/(4), where a_(n)=n^(2),(sqrt(1+(1)/(n))+sqrt(1-(1)/(n))-2) for n in N.

Let a_(n)=i^((n+1)^2) , where i=sqrt(-1)" and "n=1, 2, 3,"……….." . Then the value of a_(1)+a_(3)+a_(5)+"……….."+a_(25) is

If (1+px+x^(2))^(n)=1+a_(1)x+a_(2)x^(2)+…+a_(2n)x^(2n) . The value of a_(1)+3a_(2)+5a_(3)+7a_(4)+….(4n-1)a_(2n) when p=-3 and n in even is

If (1+px+x^(2))^(n)=1+a_(1)x+a_(2)x^(2)+…+a_(2n)x^(2n) . The value of a_(1)+3a_(2)+5a_(3)+7a_(4)+….(4n-1)a_(2n) when p=-3 and n in even is

If (1+px+x^(2))^(n)=1+a_(1)x+a_(2)x^(2)+…+a_(2n)x^(2n) . The value of a_(1)+3a_(2)+5a_(3)+7a_(4)+….(4n-1)a_(2n) when p=-3 and n in even is