If `a_(1)=1` and `a_(n+1)=(4+3a_(n))/(3+2a_(n)),nge1"and if" lim_(ntooo) a_(n)=a,"then find the value of a."`

If a_(n+1)=1/(1-a_n) for n>=1 and a_3=a_1 . then find the value of (a_2001)^2001 .

A_(i)=(x-a_(i))/(|x-a_(i)|),i=1,2,...,n," and "a_(1)lta_(2)lta_(3)lt...lta_(n). If 1lemlen,minN, then the value of L=lim_(xtoa_(m)) (A_(1)A_(2)...A_(n)) is

Let {a_n}(ngeq1) be a sequence such that a_1=1,a n d3a_(n+1)-3a_n=1 for all ngeq1. Then find the value of a_(2002.)

If (1+x-2x^(2))^(6) = 1 + a_(1)x+a_(2)x^(2) + "……" + a_(12)x^(12) , then find the value of a_(2) + a_(4) +a_(6)+ "……" + a_(12) .

If a_(1) = 2 and a_(n) - a_(n-1) = 2n (n ge 2) , find the value of a_(1) + a_(2) + a_(3)+…+a_(20) .

Let A=([a_(i j)])_(3xx3) be a matrix such that AA^T=4Ia n da_(i j)+2c_(i j)=0,w h e r ec_(i j) is the cofactor of a_(i j)a n dI is the unit matrix of order 3. |a_(11)+4a_(12)a_(13)a_(21)a_(22)+4a_(23)a_(31)a_(32)a_(33)+4|+5lambda|a_(11)+1a_(12)a_(13)a_(21)a_(22)+1a_(23)a_(31)a_(32)a_(33)+1|=0 then the value of 10lambda is _______.

If n in N such that is not a multiple of 3 and (1+x+x^(2))^(n) = sum_(r=0)^(2n) a_(r ). X^(r ) , then find the value of sum_(r=0)^(n) (-1)^(r ).a_(r).""^(n)C_(r ) .

IF a_(1),a_(2),a_(3),"...."a_(10) be in AP and h_(1),h_(2),h_(3),"...."h_(10) be in HP. If a_(1)=h_(1)=2 and a_(10)=h_(10)=3 , then find value of a_(4)h_(7) .

The Fibonacci sequence is defined by 1=a_(1)=a_(2) and a_n =a_(n-1)+a_(n-2) , n gt 2 Find (a_(n+1))/a_n for n = 1, 2, 3, 4, 5

Let alpha and beta be the roots of equation x^(2)-6x-2=0." If " a_(n)=alpha^(n)-beta^(n)," for "nge1 , "then the value of " ((a_(10))-(2a_(8)))/(2a_(9)) is equal to -