Questions from General Calculus

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

Find the sum of the series ∑∞n=1 1/n5 correct to three decimal places.

Q: Estimate ∑∞n=1 (2n + 1)-6 correct

Estimate ∑∞n=1 (2n + 1)-6 correct to five decimal places.

Q: How many terms of the series ∑∞n=1 1/

How many terms of the series ∑∞n=1 1/ [n (ln n)2] would you need to add to find its sum to within 0.01?

Q: Use the sum of the first 10 terms to approximate the sum

Use the sum of the first 10 terms to approximate the sum of the series. Estimate the error.

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: Use the sum of the first 10 terms to approximate the sum

Use the sum of the first 10 terms to approximate the sum of the series. Estimate the error.

Q: (a). Use a graph of y = 1 to show

(a). Use a graph of y = 1 to show that if sn is the nth partial sum of the harmonic series, then (b). The harmonic series diverges, but very slowly. Use part (a) to show that the sum of the first mi...

Q: Suppose ∑an and ∑bn are series with positive terms and

Suppose ∑an and ∑bn are series with positive terms and ∑bn is known to be divergent. (a). If an > bn for all n, what can you say about ∑an? Why? (b). If an < bn for all n, what can you say about ∑an?...

Q: The meaning of the decimal representation of a number 0.d1d2d3

The meaning of the decimal representation of a number 0.d1d2d3.. (where the digit di is one of the numbers 0, 1, 2, . . . , 9) is that

Q: Show that if an > 0 and ∑an is convergent,

Show that if an > 0 and ∑an is convergent, then ∑ ln (1 + an) is convergent.