Give a recursive definition of the sequence {a}, n=1, 2, 3,...if a) a₂ = 6n. b) an = 5.
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- Give a recursive definition for the set POWERS-OF-TWO = {1 2 4 8 16 ....} and use your definition to prove that the product of two POWERS-OF-TWO is also a POWER-OF-TWOGive a recursive definition for the set of all strings of a’s and b’s that begins with an a and ends in a b. Say, S = { ab, aab, abb, aaab, aabb, abbb, abab..} Let S be the set of all strings of a’s and b’s that begins with a and ends in a b. The recursive definition is as follows – Base:... Recursion: If u ∈ S, then... Restriction: There are no elements of S other than those obtained from the base and recursion of S.Solve the recursion where F(0) = 0 and F(1) = 1
- T/F 8. Without recursion, the Koch snowflake = 1 could be drawn.I. recursion to print half of the indent hourgs pattern.The Polish mathematician Wacław Sierpiński described the pattern in 1915, but it has appeared in Italian art since the 13th century. Though the Sierpinski triangle looks complex, it can be generated with a short recursive function. Your main task is to write a recursive function sierpinski() that plots a Sierpinski triangle of order n to standard drawing. Think recursively: sierpinski() should draw one filled equilateral triangle (pointed downwards) and then call itself recursively three times (with an appropriate stopping condition). It should draw 1 filled triangle for n = 1; 4 filled triangles for n = 2; and 13 filled triangles for n = 3; and so forth. API specification. When writing your program, exercise modular design by organizing it into four functions, as specified in the following API: public class Sierpinski { // Height of an equilateral triangle whose sides are of the specified length. public static double height(double length) // Draws a filled equilateral…
- Find a recursive definition for the sequence 5, 7, 10, 14, 19,... for n>1. How do I find the equation/recursive definition for this?Give a recursive definition for the set of all strings of a’s and b’s where all the strings are of odd lengths. (Assume, S is set of all strings of a’s and b’s where all the strings are of odd lengths. Then S = { a, b, aaa, aba, aab, abb, baa, bba, bab, bbb, aaaaa, ... )8- Determine if each of the following recursive definition is a valid recursive definition of a function f from a set of non-negative integers. If f is well defined, find a formula for f(n) where n is non- negative and prove that your formula is valid. a. f(0) = 2,f(1) = 3, f(n) = f(n-1)-1 for n ≥ 2 b. f(0) = 1,f(1) = 2, f(n) = 2f (n-2) for n = 2