If `(1+x)^(n) = a_(0) + a_(1)x + a_(2)x^(2) + ....+a_(n)x^(n)`, then `(1+(a_(1))/(a_(0)))(1+(a_(2))/(a_(1)))(1+(a_(3))/(a_(2)))...(1+(a_(n))/(a_(n-1)))=`

(1+x)^(n)=a_(0)+a_(1)x+a_(2)*x^(2)+......+a_(n)x^(n) then prove that

Let (1 + x)^(n) = sum_(r=0)^(n) a_(r) x^(r) . Then ( 1+ (a_(1))/(a_(0))) (1 + (a_(2))/(a_(1)))…(1 + (a_(n))/(a_(n-1))) is equal to

If a_(1),a_(2),...,a_(n)>0, then prove that (a_(1))/(a_(2))+(a_(2))/(a_(3))+(a_(3))/(a_(4))+...+(a_(n-1))/(a_(n))+(a_(n))/(a_(1))>n

If (1+x+x^(2))^(n)=a_(0)+a_(1)x+a_(2)x^(2)+...+a_(2n)x^(2n), then a_(0)+a_(2)+a_(4)+....+a_(2n) is

Let a_(1),a_(2),a_(3),...a_(n) be an AP.Prove that: (1)/(a_(1)a_(n))+(1)/(a_(2)a_(n-1))+(1)/(a_(3)a_(n-2))+......+(1)/(a_(n)a_(1))=

If (1+x+x^(2))^(n)=a_(0)+a_(1)x+a_(2)x^(2)+...a_(2n)x^(2n), then sqrt(a_(0))+sqrt(a_(1))+sqrt(a_(2))+...+sqrt(a_(2n)) is

If (1 + x)^(2n) = a_(0) + a_(1) x + a_(2) x^(2) +… + a_(2n) x^(2n) , then (a_(0) - a_(2) + a_(4) - a_(6) +…- a_(2n))^(2)+(a_(1) - a_(3) + a_(5) - a_(7) +...+a_(2n-1))^(2) is equal to

If (1-x+x^(2))^(n)=a_(0)+a_(1)x+a_(2)x^(2)++a_(2n)x^(2n) find the value of a_(0)+a_(2)+a_(4)++a_(2n)