Question
Using Weiestrass M-test, show that the following series converges uniformly.
Answer :
Word Count : 289
We will use the Weierstrass M-test to show that the series \[ \sum_{n=1}^{\infty} n^3 x^n \quad \text{for} \quad x \in \left[ -\frac{1}{3}, \frac{1}{3} \right] \] converges uniformly. ### Steps: 1. Check the general term: The general term of the series is \( f_n(x) = n^3 x^n \). 2. _______ ________ ______ _________ ____.
_______ _______ _________ _____ __________ __________ ______ _____ ________ _______ ___.
_________ ______ __________ _______ _________ ___ ____ ______ __________ ___ _______ ______.
_________ ________ ________ __________ ________ ______ ________ ________ ____ __________.
______ ________ _____ _________ _______ __________ ______ _________ _______ __________.
__________ _________ _______ __________ __________ ________ ________ ______ _________.
____ _____ ___ ____ __________ ______ _______ ____ _______ _____ _________ __________.
___ _______ ______ __________ ________ _______ __________ _________ ________ _______.
____ ______ _____ _________ ________ _________ _______.
_______ ________ ________ ____ ________ ______ __________ ____ ____ ______.
___ ____ ________ ___ ______ _______ ___ __________ _____ _______.
__________ ___ ______ ________ ______ _______ _________ __________ _____ ___ ______.
_____ __________ ________ __________ ______ _______ ________.
________ _________ _________ ____ _____.
________ ________ _________ _______ _____ ____ __________ ___ ______ ________ _____ ______.
__________ __________ ______ ___ _________ ___ __________ _______ _________ ______.
_______ ________ _________ ____ __________ _____.
__________ ___ ________ _______ _______ __________.
________ ________ ________ ________ ______ ___.
_____ _________ _________ _______ ______ __________ _____ __________ ___.
_________ __________ _________ _________ _______ _______.
__________ ________ _________ ________ _______ _________ ____ ___ ______ ___ ______ ______.
____ _________ ______ __________ ______ ____ _________ _____ _____ ___ _____ ___.
________ ______ ___ ______ ________ ________ ______ ___.
_____ ___ ____ ______ ___ __________ __________ _______ __________ ___ ___ __________.
____ _______ __________ ________ ___ ____.
______ _____ _________ ________ __________ ____ _________.
Get Full Answer on WhatsApp
We will use the Weierstrass M-test to show that the series \[ \sum_{n=1}^{\infty} n^3 x^n \quad \text{for} \quad x \in \left[ -\frac{1}{3}, \frac{1}{3} \right] \] converges uniformly. ### Steps: 1. Check the general term: The general term of the series is \( f_n(x) = n^3 x^n \). 2. _______ ________ ______ _________ ____.
_______ _______ _________ _____ __________ __________ ______ _____ ________ _______ ___.
_________ ______ __________ _______ _________ ___ ____ ______ __________ ___ _______ ______.
_________ ________ ________ __________ ________ ______ ________ ________ ____ __________.
______ ________ _____ _________ _______ __________ ______ _________ _______ __________.
__________ _________ _______ __________ __________ ________ ________ ______ _________.
____ _____ ___ ____ __________ ______ _______ ____ _______ _____ _________ __________.
___ _______ ______ __________ ________ _______ __________ _________ ________ _______.
____ ______ _____ _________ ________ _________ _______.
_______ ________ ________ ____ ________ ______ __________ ____ ____ ______.
___ ____ ________ ___ ______ _______ ___ __________ _____ _______.
__________ ___ ______ ________ ______ _______ _________ __________ _____ ___ ______.
_____ __________ ________ __________ ______ _______ ________.
________ _________ _________ ____ _____.
________ ________ _________ _______ _____ ____ __________ ___ ______ ________ _____ ______.
__________ __________ ______ ___ _________ ___ __________ _______ _________ ______.
_______ ________ _________ ____ __________ _____.
__________ ___ ________ _______ _______ __________.
________ ________ ________ ________ ______ ___.
_____ _________ _________ _______ ______ __________ _____ __________ ___.
_________ __________ _________ _________ _______ _______.
__________ ________ _________ ________ _______ _________ ____ ___ ______ ___ ______ ______.
____ _________ ______ __________ ______ ____ _________ _____ _____ ___ _____ ___.
________ ______ ___ ______ ________ ________ ______ ___.
_____ ___ ____ ______ ___ __________ __________ _______ __________ ___ ___ __________.
____ _______ __________ ________ ___ ____.
______ _____ _________ ________ __________ ____ _________.
Get Full Answer on WhatsApp
Related Questions
Verify Bozano–Weierstrass Theorem for the following sets:
i) Set of non-negative integers.
ii) Interval [− ,1 ∞]
Use Cauchy’s mean value theorem to prove that:
Show that is conditionally convergent.
Find a and b such that
Test the following series for convergence,
(i)
(ii)
Check whether the set of integers is countable or not.
Check whether the exists or not?
IGNOU NEWS
Assignment Submission Last Date Extended Till 30 June 2026 Click Here★★★IGNOU June 2026 TEE Date Sheet Released Click Here★★★