Find the sum (n=5, to infinity) of the series (n2 -n)/2n

Find the sum (n=5, to infinity) of the series (n² -n)/2ⁿ

Expert Solution

milcah answered 1 year ago

Determine if the following series converge or diverge. If it converges, find the sum. a. ∑n=(3^n+1)/(2n)...

Determine if the following series converge or diverge. If it converges, find the sum. a. ∑n=(3^n+1)/(2n) (upper limit of sigma∞, lower limit is n=0) b.∑n=(cosnπ)/(2) (upper limit of sigma∞ , lower limit is n= 1 c.∑n=(40n)/(2n−1)^2(2n+1)^2 (upper limit of sigma ∞ lower limit is n= 1 d.)∑n = 2/(10)^n (upper limit of sigma ∞ , lower limit of sigma n= 10)

1) Find the radius of convergence and interval of convergence of the given series Σ x^2n/n!...

1) Find the radius of convergence and interval of convergence of the given series Σ x^2n/n! 2) Find the power series representation of f(x)=(x-1)/(x+2) first then find its interval of convergence.

1. Test the series below for convergence using the Root Test. ∞∑n=1 (2n/7n+5)^n The limit of...

1. Test the series below for convergence using the Root Test. ∞∑n=1 (2n/7n+5)^n The limit of the root test simplifies to lim n→∞ |f(n)| where f(n)= The limit is: Based on this, the series Diverges Converges 2. Multiple choice question. We want to use the Alternating Series Test to determine if the series: ∞∑k=4 (−1)^k+2 k^2/√k5+3 converges or diverges. We can conclude that: The Alternating Series Test does not apply because the terms of the series do not alternate. The...

Use the formula for the sum of the first n terms of an arithmetic series to find the sum of the first eleven terms of the arithmetic series 2.5, 4, 5.5, … .

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

Let n be a positive integer. Prove that two numbers n2+3n+6 and n2+2n+7 cannot be prime...

Let n be a positive integer. Prove that two numbers n2+3n+6 and n2+2n+7 cannot be prime at the same time.

Determine the sum of the series ∑n=1∞ ( 6n)/(n+2) if possible. (If the series diverges, enter...

Determine the sum of the series ∑n=1∞ ( 6n)/(n+2) if possible. (If the series diverges, enter 'infinity', '-infinity' or 'dne' as appropriate.)

1a. Proof by induction: For every positive integer n, 1•3•5...(2n-1)=(2n)!/(2n•n!). Please explain what the exclamation mark...

1a. Proof by induction: For every positive integer n, 1•3•5...(2n-1)=(2n)!/(2n•n!). Please explain what the exclamation mark means. Thank you for your help! 1b. Proof by induction: For each integer n>=8, there are nonnegative integers a and b such that n=3a+5b

5. Without using the method of mathematical induction, prove that 5^n − 3^n + 2n is...

5. Without using the method of mathematical induction, prove that 5^n − 3^n + 2n is divisible by 4 for all natural n.

Use the formula for the sum of the first n terms of a geometric series to find S9 for the series 12, 6, 3, 3/2 , …

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