HELP! this is for geometry, i really need help on number 13 but if you can help me with the others.
1 answer:
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Answer:
Required result : (a) Divergent. (b) Convergent. (c) Divergent, (d) Not exists. (e) Not exists.
Step-by-step explanation:
By the definition of integral test the series for a integer n and a continuous function f(x) which is monotonic decreasing in then the infinite series
converges or diverges if and only if the improper integral
converges or diverges.
Given,
(a)
Then,
Let,
By using integral calculator we get,
which is divergent. Therefore given (2) is divergent and so is (1).
(b)
Then in integral form,
Thus given series (3) is convergent.
(c)
Then in integral form,
Now let,
Applying integral calculator we get,
which is divergent and thus,
is divergent. So, given series (4) is divergent.
(d)
which is in integral form,
during integration since there is no any antiderivative, the result could not be found.
(e)
Integral form is,
Let,
Using integral calculator we get,
But,
not exists.