# How do you solve the series #sin (1/n)# using comparison test?

By comparing it with

The sine function has this weird property that for very small values of

You can see this easily by plotting the graph for

You can see that when

So this also means that for very small values of

When does

We also know that

By signing up, you agree to our Terms of Service and Privacy Policy

To solve the series ( \sin\left(\frac{1}{n}\right) ) using the comparison test:

- Choose a series ( b_n ) that is easier to evaluate and for which it is known whether it converges or diverges.
- Establish a comparison between the given series ( \sin\left(\frac{1}{n}\right) ) and the chosen series ( b_n ).
- Show that ( | \sin\left(\frac{1}{n}\right) | \leq | b_n | ) for all ( n ) beyond some index ( N ).
- Use the convergence or divergence of the series ( b_n ) to determine the convergence or divergence of ( \sin\left(\frac{1}{n}\right) ).

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- Prove that for #n > 1# we have #1 xx 3 xx 5 xx 7 xx cdots xx(2n-1) < n^n#?
- How do you determine whether the sequence #a_n=(n+1)^n/n^(n+1)# converges, if so how do you find the limit?
- How do you find #lim costheta/(pi/2-theta)# as #theta->pi/2# using l'Hospital's Rule?
- How do you test the improper integral #int(x-1)^(-2/3)dx# from #[0,1]# and evaluate if possible?
- How do you find the nth term of the sequence #1, 3, 6, 10, 15,...#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7