Questions from Calculus

Q: Find the sum of the given infinite series if it is convergent

Find the sum of the given infinite series if it is convergent. 1/m – 1/m2 + 1/m3 – 1/m4 + 1/m5 - …, where m is a positive number

Q: Find the sum of the given infinite series if it is convergent

Find the sum of the given infinite series if it is convergent. 1 + 2 + 22/2! + 23/3! + 24/4! + …

Q: Find the sum of the given infinite series if it is convergent

Find the sum of the given infinite series if it is convergent. 1 + 1/3 + 1/2! (1/3)2 + 1/3! (1/3)3 + 1/4! (1/3)4 + …

Q: Use properties of convergent series to find a ∑k=0

Use properties of convergent series to find a ∑k=0∞ (1 + 2k)/3k.

Q: Find ∑k=0∞ (3k + 5k)/7k

Find ∑k=0∞ (3k + 5k)/7k.

Q: Determine if the given series is convergent. ∑k=

Determine if the given series is convergent. ∑k=1∞ 1/k3

Q: Determine if the given series is convergent. ∑k=

Determine if the given series is convergent. ∑k=1∞ 1/3k

Q: The third remainder for f (x) at x = 0

The third remainder for f (x) at x = 0 is R3 (x) = f (4) (c)/4! x4, where c is a number between 0 and x. Let f (x) = cos x, as in Check Your Understanding Problem 11.1. (a) Find a number M such that |...

Q: Determine if the given series is convergent. ∑k=

Determine if the given series is convergent. ∑k=1∞ (ln k)/k

Q: Determine if the given series is convergent. ∑k=

Determine if the given series is convergent. ∑k=0∞ k3/(k4 + 1)2