decide whether the given sequence or series is convergent?

Question

An=(3n)/(10n+7)

For both of the following decide whether the given sequence or series is convergent or divergent. If convergent, enter the limit (for a sequence) or the sum (for a series). If divergent, enter INF if it diverges to infinity, MINF if it diverges to minus infinity, or DIV otherwise.

A. the series the sum n=1 to infinity (An)

B. the sequence {An}

ok i'm pretty sure that the answer for A is 3/10 because i just divided by n, but im not sure what B is. I think the answer is 1

Answer 1

B. the sequence does converge to 3/10. By dividing top and bottom by n you get the expression 3/(10 + 7/n) which clearly goes to 3/(10 + 0) as n goes to infinity.

A. Note that every term in the sequence is greater than 3/17. Therefore, the sum of the first k terms will be greater than (3/17)*(k); the infinte series diverges to infinity.

Answer 2

The answer to B, not A is 3/10... This is your typical limit problem

The answer to A is infinity... if Bn = sum n=1 to infinity (An), then Bn will converge if and only if An converges to zero. This should make intuitive sense... if An converges to 3/10, then for each additional n you are adding 3/10 to the total sum... given enough additions of 3/10 you will eventually surpass any number in the real numbers....