Questions from General Calculus

Q: Determine whether the sequence is convergent or divergent. If it is

Determine whether the sequence is convergent or divergent. If it is convergent, find its limit.

Q: Determine whether the sequence is convergent or divergent. If it is

Determine whether the sequence is convergent or divergent. If it is convergent, find its limit.

Q: A sequence is defined recursively by the equations a1 = 1,

A sequence is defined recursively by the equations a1 = 1, an+1 = 1/3(an + 4). Show that {an} is increasing and an < 2 for all n. Deduce that {an} is convergent and find its limit.

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

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

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

Determine whether the series is convergent or divergent. ∑∞n=1 n2 +1/n3 + 1

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

Determine whether the series is convergent or divergent. ∑∞n=1 n3/5n

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

Sketch the curve and find the area that it encloses. r2 = 4 cos 2θ

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

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

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

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

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

Determine whether the series is convergent or divergent. ∑∞n=1 ln (n/3m + 1)