Consider the following recursive definition: if n=1 F(n)= | Fin - 1) +2 if n >...
Give a recursive definition of the sequence {an}, n = 1, 2, 3,... if an = n2 커-1, an-an-1+2n, for all n>1 어=1, an = an-1+2n-1, for all n21 an = an-1+2n-1. for all n21 gel, an=an-1+2n-1, for all n>1 -1, an- an-1+2n-1, for all n2o
From mathematics, we know that 20 = 1 and 25 = 2*24. In general, xo = 1 and xn = x*xn-1 for integer x, and integer n>O. Write the recursive function power(x.n) that takes two integers an returns the value of . No credit will be given if the function is not recursive. >>power(3,4) 81 >>power(4,2) 16
+ – for n > 1, subject to Problem 5 (6 pts): Solve the recursive equation T(n the initial condition T(1) = 0.
Problem 7: Prove that for all integers n > 2, n+1 n 10-11 - n n +
Prove that is an integer for all n > 0.
Use the Principle of Mathematical Induction to prove that (2i+3) = n(n + 4) for all n > 1.
Prove this using the definition R7: log(n*) is O(log n) for any fixed x > 0
-. Show that if x ~ Unif(a, β) and μ-E(X) (so μ-(a + β)/2), then for integers r > 0, 0 r odd 12
2. Consider the Fibonacci sequence {rn} given by x1 = 1, 22 = 1 and Xn = In-1 + In-2 for n > 3. Using Principle of Mathematical Induction show that for any n >1, *-=[(4725)* =(4,799"]
2. Prove that if n > 1, then 1(1!) + 2(2!) + ... + n(n!) = (n + 1)! - 1.