3. Now estimate how far T is from y for a given integer k. Prove that for k > 10 < T – y< by using the following steps.(a) Show that In(k+1) – In(k) < .(b) Use the result from part (a) to show that for any integer k,11Tk – Tk+1 <k|-|k +1°(c) For any integers k and j such that j > k, show that11T – T; <k(Hint: Try to use a telescoping sum.)(d) Apply the limit to both sides of the inequality in (c) to conclude that1Tk – <.(e) Estimate y to an accuracy of within 0.001.

To show, 0<Tk-γ≤1k for a given integer k≥1 where limk→∞Tk=γ. Consider the Taylor series expansion…

3. Now estimate how far T is from y for a given integer k. Prove that for k > 0 < Tx – y < by using the following steps. (a) Show that In(k +1) – In(k) < (b) Use the result from part (a) to show that for any integer k, 1 1 T – Tk+1 < k k +1 (c) For any integers k and j such that j > k, show that 1 1 T – T; < k (Hint: Try to use a telescoping sum.) (d) Apply the limit to both sides of the inequality in (c) to conclude that 1 (e Estimate to an 9ccuracy of withim 0.001

3. Now estimate how far T is from y for a given integer k. Prove that for k > 0 < Tx – y < by using the following steps. (a) Show that In(k +1) – In(k) < (b) Use the result from part (a) to show that for any integer k, 1 1 T – Tk+1 < k k +1 (c) For any integers k and j such that j > k, show that 1 1 T – T; < k (Hint: Try to use a telescoping sum.) (d) Apply the limit to both sides of the inequality in (c) to conclude that 1 (e Estimate to an 9ccuracy of withim 0.001

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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