Questions from General Calculus

Q: For what values of does the series ∑∞n=1(

For what values of does the series ∑∞n=1(ln x)n converge?

Q: Find the sum of the series ∑∞n=1 (-1

Find the sum of the series ∑∞n=1 (-1)n+1 /n5 correct to four decimal places.

Q: (a). Find the partial sum s5 of the series ∑∞

(a). Find the partial sum s5 of the series ∑∞n=1 1/n6 and estimate the error in using it as an approximation to the sum of the series. (b). Find the sum of this series correct to five decimal places....

Q: Use the sum of the first eight terms to approximate the sum

Use the sum of the first eight terms to approximate the sum of the series∑∞n=1 (2 + 5n)-1. Estimate the error involved in this approximation.

Q: (a). Show that the series ∑∞n=1nn/(

(a). Show that the series ∑∞n=1nn/(2n)! is convergent. (b). Deduce that limn→∞ nn/(2n)! = 0.

Q: Prove that if the series ∑∞n=1 an is absolutely

Prove that if the series ∑∞n=1 an is absolutely convergent, then the series ∑∞n=1 (n + 1/n)an is also absolutely convergent.

Q: Find the radius of convergence and interval of convergence of the series

Find the radius of convergence and interval of convergence of the series.

Q: Find the radius of convergence and interval of convergence of the series

Find the radius of convergence and interval of convergence of the series.

Q: Sketch the curve and find the area that it encloses.

Sketch the curve and find the area that it encloses. r = 2 cos 3θ

Q: Find the radius of convergence and interval of convergence of the series

Find the radius of convergence and interval of convergence of the series.