An alternating series
converges if
is monotonic and
as
. Here
.
Let
. Then
, which is positive for all
, so
is monotonically increasing for
. This would mean
must be a monotonically decreasing sequence over the same interval, and so must
.
Because
is monotonically increasing, but will still always be positive, it follows that
as
.
So,
converges.
Answer:
a red
Step-by-step explanation:
A bag contains 7 red marbles, 5 blue marbles, and 2 green marbles. What is the probability of choosing a blue marble when one marble is drawn?
Answer:
4/(√7 + √3)
Step-by-step explanation:
=> Multiply and divide by (√7-√3)
=> 4(√7 - √3)/((√7 + √3)(√7 - √3)
=> 4(√7 - √3)/((√7)² - (√3)²)
=> 4(√7 - √3)/((7) - (3))
=> 4(√7 - √3)/4
=> √7 - √3
Answer:
Please check explanations for answer
Step-by-step explanation:
Here, we want to differentiate between inverse and direct proportion
Let x and y be two quantities
If they are directly proportional;
x/y = k
x = ky
where k is proportionality constant
If inversely;
xy = k
In verbal terms;
For direct proportionality, when one value increase, the other too does so and vice versa
For inverse, when one value inverse, the other decrease