Find the value of ∑(−1)^n/(3n+1) from n=0 to ∞

Expert Solution

milcah answered 3 years ago

1- Show that (n^3+3n^2+3n+1) / (n+1) is O (n2 ). Use the definition and proof of...

1- Show that (n^3+3n^2+3n+1) / (n+1) is O (n2 ). Use the definition and proof of big-O notation. 2- Prove using the definition of Omega notation that either 8 n is Ω (5 n ) or not. please help be with both

def seq3np1(n): """ Print the 3n+1 sequence from n, terminating when it reaches 1. args: n...

def seq3np1(n): """ Print the 3n+1 sequence from n, terminating when it reaches 1. args: n (int) starting value for 3n+1 sequence return: None """ while(n != 1): print(n) if(n % 2) == 0: # n is even n = n // 2 else: # n is odd n = n * 3 + 1 print(n) # the last print is 1 def main(): seq3np1(3) main() Using the provided code, alter the function as follows: First, delete the print statements...

Derive the Sackur-Tetrode equation starting from the multiplicity givenin Ch. 2: Ω =(1/N!)(V^{N}/h^{3N})(pi^{3N/2}/3N^{2}!)(2mU)^{3N/2} The Sackur-Tetrode equation...

Derive the Sackur-Tetrode equation starting from the multiplicity givenin Ch. 2: Ω =(1/N!)(V^{N}/h^{3N})(pi^{3N/2}/3N^{2}!)(2mU)^{3N/2} The Sackur-Tetrode equation is: S=Nk[ln((V/N)((4pi*m*U)/(3Nh^{2}))^{3/2})+(5/2)]

what is the radius of convergence for sum {0} to {infinity} x^3n / 27^n

6a. Show that 2/n = 1/3n + 5/3n and use this identity to obtain the unit...

6a. Show that 2/n = 1/3n + 5/3n and use this identity to obtain the unit fraction decompositions of 2/25 , 2/65 , and 2/85 as given in the 2/n table in the Rhind Mathematical Papyrus. 6b. Show that 2/mn = 1/ (m ((m+n)/ 2 )) + 1/ (n ((m+n)/ 2 )) and use this identity to obtain the unit fraction decompositions of 2/7 , 2/35 , and 2/91 as given in the 2/n table in the Rhind Mathematical Papyrus....

1. a) Prove that if n is an odd number then 3n + 1is an even...

1. a) Prove that if n is an odd number then 3n + 1is an even number. Use direct proof. b) Prove that if n is an odd number then n^2+ 3 is divisible by 4. Use direct proof. 2. a) Prove that sum of an even number and an odd number is an odd number. Use direct proof. b) Prove that product of two rational numbers is a rational number. Use direct proof. 3. a) Prove that if n2is...

Question

Find the value of ∑(−1)^n/(3n+1) from n=0 to ∞

Solutions

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1- Show that (n^3+3n^2+3n+1) / (n+1) is O (n2 ). Use the definition and proof of...

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