Questions from General Calculus

Q: Determine whether the series is convergent or divergent. ∑∞n

Determine whether the series is convergent or divergent. ∑∞n=1 1/√n3 + 1

Q: Determine whether the series is absolutely convergent. ∑∞n=

Determine whether the series is absolutely convergent. ∑∞n=1 n2/2n

Q: If k is a positive integer, find the radius of convergence

If k is a positive integer, find the radius of convergence of the series

Q: Determine whether the series is absolutely convergent. ∑∞n=

Determine whether the series is absolutely convergent. ∑∞n=1 (-1)n-12nn4

Q: Determine whether the series is absolutely convergent. ∑∞n=

Determine whether the series is absolutely convergent. ∑∞n=1 102/(n + 1)42n+1

Q: Determine whether the series is absolutely convergent. ∑∞n=

Determine whether the series is absolutely convergent. ∑∞n=1 sin4n/4n

Q: A function f is defined by f (x) = 1

A function f is defined by f (x) = 1 + 2x + x2 + 2x3 + x4 + … that is, its coefficients are c2n = 1 and c2n+1 = 2 for all n > 0. Find the interval of convergence of the series and find an explicit for...

Q: Is it possible to find a power series whose interval of convergence

Is it possible to find a power series whose interval of convergence is [0, ∞]? Explain.

Q: A series ∑an is defined by the equations Determine whether ∑

A series ∑an is defined by the equations Determine whether ∑an converges or diverges

Q: Show that if we want to approximate the sum of the series

Show that if we want to approximate the sum of the series ∑∞n=1 n-1.001 so that the error is less than 5 in the ninth decimal place, then we need to add more than 1011.301 terms!