1. ## Series

Determine whether the series is convergent or divergent. If it is convergent, find its sum.

1) Sum of k(k+2) / (k+3)^2 with k = 1 to infinity.

2) Sum of (cos 1)^k with k = 1 to infinity.

can someone help me with these? thanks.

2. For #1 apply the first test for convergence: $\displaystyle \left( {a_n } \right) \to 0$???

For #2, How large is cos(1)?

3. Originally Posted by xfyz
Determine whether the series is convergent or divergent. If it is convergent, find its sum.

1) Sum of k(k+2) / (k+3)^2 with k = 1 to infinity.
this sum diverges to infinity.

2) Sum of (cos 1)^k with k = 1 to infinity.

can someone help me with these? thanks.
i don't know i believe it is convergent though, but it may not be, the reverse implication of the theorem Plato hinted at is not always true

EDIT: Ah, i do know. it's a geometric series. finally got Plato's hint...stupid me

4. Originally Posted by Plato
For #1 apply the first test for convergence: $\displaystyle \left( {a_n } \right) \to 0$???

For #2, How large is cos(1)?
For the 1st one, i think the book wants me to use the ar^n-1 method ?
In your reply, are you telling me to just take the limit as n goes to infinity of that equation?

2) what do u mean how large is cos 1 ? cos 1 is close to .5 .. am i supposed to consider the domain? -1 > x > 1 ?

5. Originally Posted by xfyz
For the 1st one, i think the book wants me to use the ar^n-1 method ?
In your reply, are you telling me to just take the limit as n goes to infinity of that equation?
yes, take the limit of the formula
2) what do u mean how large is cos 1 ? cos 1 is close to .5 .. am i supposed to consider the domain? -1 > x > 1 ?
his point is, it's a convergent geometric sequence.

ah, there's the answer! find the formula for the sum of a geometric series

6. Originally Posted by Jhevon
yes, take the limit of the formula
his point is, it's a convergent geometric sequence.

ah, there's the answer! find the formula for the sum of a geometric series
a / 1-r

cos 1 / 1 - cos 1 = 1.175

is this correct?

7. Originally Posted by xfyz
a / 1-r

cos 1 / 1 - cos 1 = 1.175

is this correct?
yes