Let `a_(1), a_(2), …………….,a_(n)` be fixed real numbers and define a function `f(x) = (x-a_(1))(x-a_(2))…….(x-a_(n))`. What is `lim_(x rarr a_(1)) f(x)?` For some `a ne a_(1), a_(2),……a_(n)` compute `lim_(x rarr a) f(x)`

If the function f(x) satisfies lim_(x rarr 1) (f(x)-2)/(x^(2)-1) = pi , evaluate lim_(x rarr 1) f(x)

If fthe function f(x) satisfies lim_(x rarr 1) (f(x) - 2)/(x^2 - 1) = pi , evaluate lim_(x rarr 1) f(x).

If a_(1), a_(2), a_(3),…….,a_(20) are in AP and a_(1) + a_(20) = 45 , then a_(1) + a_(2) + a_(3)+……+a_(20) is equal to

If a_(1), a_(2), …, a_(50) are in GP, then " "(a_(1)-a_(3)+a_(5)-…+a_(49))/(a_(2)-a_(4)+a_(6)-…+a_(50)) is equal to :

Write the first three terms of the sequence defined by a_(1)= 2 ,a_(n+1) = (2a_(n)+3)/(a_(n)-:2)

Let a_(1),a_(2),a_(3),a_(4) and a_(5) be such that a_(1), a_(2) and a_(3) are in A.P. a_(2) ,a_(3) and a_(4) are in G.P and a_(3) ,a_(4) and a_(5) are in H.P . Then a_(1) ,a_(3) and a_(5) are in

If a_(1), a_(2), a_(3),….,a_(n) are in AP and a_(1) = 0 , then the value of ((a_(3))/(a_(2)) + (a_(4))/(a_(3)) +...+(a_(n))/a_(n-1))-a_(2) ((1)/(a_(2)) + (1)/(a_(3))+...+(1)/(a_(n-2))) is equal to a) (n-2) + (1)/((n-2)) b) (1)/((n-2)) c)(n - 2) d)(n - 1)

Let a_(1) ,a_(2) ,a_(3) ,cdots ,a_(n) are in A.P such that a_(n) =100 , a_(10)- a_(39 ) = (3)/(5) then find the 15^(th) term of A.P. from end.

Let (1+x)^(n) = 1+a_(1)x + a_(2)x^(2) + ……+ a_(n)x^(n) . If a_(1), a_(2) and a_(3) are in AP, then the value of n is