Hey! I need some help again with series. I hate this topic lol
how would you do these problems
1. Finde the range of values for which the following series is convergent or divergent:
2. Investigate the convergence of the series
for
sorry to flood you with questions, its because I have a test very soon on this.
and want to get a good mark
thank you!
Hello, Enita!
I wanted to know, say you had: .
How do you know that: .
How would you work out ?
You do it by Inspection . . . and a bit of Experience.
. . You're expected to "eyeball" it.
The numerators are:
. . You recognize them as consecutive odd numbers.
And you're supposed to know the general formula: .
The denominators are:
. . which you should recognize as consecutive powers of 2.
Since it begins with , the first denominator must be .
. . So the denominators are: .
Therefore: .
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
Another example: .
The numerators are:
They "go up by 3" . . . This tells us that the formula is:
The first term is
So when , we have: .
. . Hence, the formula for the numerator is: .
The denominators are:
. . They go up by a multiple of 3. .The formula is
Since it begins with , the first denominator is
. . So the denominators are: .
Therefore, the general term is: .
Hope this helps . . .