For what values of #r# does the sequence #a_n = (nr)^n# converge ?
By signing up, you agree to our Terms of Service and Privacy Policy
The sequence (a_n = (nr)^n) converges if and only if (|nr| < 1). Therefore, it converges for values of (r) such that (-\frac{1}{n} < r < \frac{1}{n}), excluding (r = 0).
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.
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