Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is inconclusive, determine the convergence or divergence of the series using other methods. [infinity] n = 1 n2/5n n = 1
lim n→[infinity] an + 1/an =
a. converges
b. diverges

Step-by-step explanation:

If is a series, for the series to converge/diverge according to ratio test, the following conditions must be met.

If < 1, the series converges absolutely

If , the series diverges

If , the test fails.

Given the series

To test for convergence or divergence using ratio test, we will use the condition above.

aₙ₊₁/aₙ =

note that any constant dividing infinity is equal to zero

Since The limit of the sequence given is less than 1, hence the series converges.

3

step-by-step explanation:

in standard form:

a= dictionaries

b= maps

you have to buy 3 dictionaries, so put a 3 next to the a (dictionaries) so that you can multiply them by each other.

a3+b= 60 (the amount of money you have)

we already know the cost of a=15 so replace a with $15

($15 x 3)+b=60

multiply 15 and 3 to get $45 and replace it with $45

45+b=60

and then replace b with 15 to get the total:

45+15=60

that means you have $15 left after buying 3 dictionaries.

15 divided by the cost of a map ($5) equals 3.

so you can buy 3 maps.

sorry if it was confusing!