# The series #sum_(n=1)^oo x^n/10^n # converges for #|x| lt beta#, find #beta#?

We can apply d'Alembert's ratio test:

Suppose that;

Then

if L < 1 then the series converges absolutely; if L > 1 then the series is divergent; if L = 1 or the limit fails to exist the test is inconclusive.

Our series is;

So our test limit is:

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

The series (\sum_{n=1}^{\infty} \frac{x^n}{10^n}) converges if (|x| < 10). Therefore, (\beta = 10).

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.

- How do you find the nth partial sum, determine whether the series converges and find the sum when it exists given #1-2+3-4+...+n(-1)^(n-1)#?
- What does the alternating harmonic series converge to?
- How do you determine if #a_n=(1-1/8)+(1/8-1/27)+(1/27-1/64)+...+(1/n^3-1/(n+1)^3)+...# converge and find the sums when they exist?
- The integral #int_0^a (sin^2x)/x^(5/2)dx# converges or diverges ?
- How do you find #lim sin(2x)/x# as #x->0# using l'Hospital's Rule?

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