Using only the e – N definition of convergence prove that the sequence (an)nENgiven by the formula5n77nan =converges to 0. (Hint: It may be helpful to prove first an inequality that saysthat the geometric quantity in the denominator grows a lot faster than thepolynomial in the numerator.)

We are given a sequence as : an = 5n7/7n And we have to show that the given sequence converges to 0…

Answered: Using only the € – N definition of…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Using only the € – N definition of convergence prove that the sequence (a,)nɛN given by the formula 5n7 7n an converges to 0. (Hint: It may be helpful to prove first an inequality that says that the geometric quantity in the denominator grows a lot faster than the polynomial in the numerator.)