Question

Explain why the integral test can't be used to determine whether the series is convergent.

Answer 1

A group of environmentalists were discussing the benefits and drawbacks associated with using fossil fuels. Which argument best fits the conversation?
Fossil fuels are cheaper than alternative forms of energy.Fossil fuel reserves will never be depleted.Fossil fuels are easily renewed. Fossil fuel use does not affect the environment.

Answer 2

For applying integral test, our first condition should be the expression must be

(a)continuous

(b) Positive

(c) Decreasing

Explanation:

For applying integral test, our first condition should be the expression must be

(a)continuous

(b) Positive

(c) Decreasing

If anyone of these conditions are not fulfilled then we can't apply integral test

And if the value of integral is finite ....then that is convergent series

And if the value of integral is infinite ....then that is divergent series

For example:

Suppose, we are given

`\sum _(n=0)^(\infty )\:\left(sin\left(n\right)\right)`

we know that

sin(n) is always continuous

but value of sin(n) always oscillates between -1 and 1

so, it can neither be decreasing nor positive value

So, we can not apply integral test here