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.
this sum diverges to infinity.
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 true2) Sum of (cos 1)^k with k = 1 to infinity.
can someone help me with these? thanks.
EDIT: Ah, i do know. it's a geometric series. finally got Plato's hint...stupid me
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 ?
yes, take the limit of the formula
his point is, it's a convergent geometric sequence.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 ?
ah, there's the answer! find the formula for the sum of a geometric series