For the following, write its recursive definition:

A sequence {a^n} of real numbers is defined recursively by a_1=2 for n ≥ 2, a_n=(2+1∙a_1^2+2∙a_2^2+⋯+(n-1) a_(n-1)^2)/n Determine a_(2,) a_3, and a_4. Show all work. Clearly, a_n is a rational number for each n ϵ N. Based on the information in a), however, what conjecture does this suggest?

If sequence a_n of positive numbers in increasing, then it is not bounded. TRUE or FALSE

Not sure why but my answer for a^6 is marked incorrect. Please help me with the correct answer.

What is the generating function for the sequence {ck},where ck represents the number of ways to make changefor k pesos using bills worth 10 pesos, 20 pesos, 50 pesos,and 100 pesos?

Evaluate the sum from k=0 to 4 of ((-1)^k(k+3)^2+3)

Evaluate the Limit of the sequence

Suppose An = 2n^2 + 6n + 6. Find the closed formula for the sequence of differences by computing An - An-1 * An - An-1.

A sequence {a„}1 satisfies a1 = 1, a2 = 1 and 6 an = max {an-1, an-2} – min {an-1, an-2} for n > 3. Select all what applies to the sequence {an}-ı from the following list. (Remember: if a > b then max {a, b} = a and min {a, b} = b) (A) Diverge to -00 (B) Alternating. (C) Divergent (D) Bounded below.

Find the value of the number in the 75th term in this sequences: 5/2, 5, 10, 20, 40, 80, .._? * O 4.72 x 10^22 O 5.90 x 10^21 O 9.44 x 10^22 O 1.89 x 10^23