Write a general polynomial `q(z)` of degree n with coefficients that are `b_(0),b_(1),b_(2), . . .. b_(n)`,
What are the conditions on `b_(0),b_(1),b_(2), . . .. b_(n)` ?

Show that log_(b)(1/(b^n)) = -n

Let the sequence ltb_(n)gt of real numbers satisfy the recurrence relation b_(n+1)=1/3(2b_(n)+(125)/(b_(n)^(2))),b_(n)ne0. Then find lim_(ntooo) b_(n).

Find the value of n so that (a^(n+1)+b^(n+1))/(a^(n)+b^n) may be the geometric mean between a and b.

Find the value of n so that (a^(n+1)+b^(n+1))/(a^n+b^n) may be the geometric mean between a and b.

If log_(b) n = 2 and log_(n) 2b = 2 , then find the value of b.

The sum of first n terms of a series is n^(2) + an + b . Show that b = 0 and the series is in A.P.

If a≡b (mod n), then state whether a^2≡b^2 (mod n)

If the ratio of the remainders when the polynomial (x^(2m)+1) is successively divided by (x + a) and (x + b), be b : a, prove that (a^(n)-b^(n))/(b-a)=1 , where n = 2m + 1 and m inN .

If a_(n) and b_(n) are positive integers and a_(n)+sqrt2b_(n)=(2+sqrt2)^(n) , then lim_(nrarroo) ((a_(n))/(b_(n))) =

Show that two lines a_(1)x + b_(1) y+ c_(1) = 0 " and " a_(2)x + b_(2) y + c_(2) = 0 " where " b_(1) , b_(2) ne 0 are : (i) Parallel if a_(1)/b_(1) = a_(2)/b_(2) , and (ii) Perpendicular if a_(1) a_(2) + b_(1) b_(2) = 0 .