M = i=q+1 Compare this to a geometric series and use the formula for sum of geometric series to show that M< ÷. Make sure that you account for the fact that the series starts at i = q + 1. Note: This is the main step in the proof. Note that it's not enough to just show that the given series is convergent, we are also asking you to find an upper bound for the actual infinite sum. ) Explain exactly why M cannot be less than ÷. ecause our initial assumption has lead us to an absurd and contradictory assertion, we conclude that the initial sumption must have been wrong. So e must have been a irrational number to begin with!
M = i=q+1 Compare this to a geometric series and use the formula for sum of geometric series to show that M< ÷. Make sure that you account for the fact that the series starts at i = q + 1. Note: This is the main step in the proof. Note that it's not enough to just show that the given series is convergent, we are also asking you to find an upper bound for the actual infinite sum. ) Explain exactly why M cannot be less than ÷. ecause our initial assumption has lead us to an absurd and contradictory assertion, we conclude that the initial sumption must have been wrong. So e must have been a irrational number to begin with!
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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Transcribed Image Text:M =
i=q+1
1
Compare this to a geometric series and use the formula for sum of geometric series to show that M < ÷. Make
sure that you account for the fact that the series starts at i = q +1.
Note: This is the main step in the proof. Note that it's not enough to just show that the given series is
convergent, we are also asking you to find an upper bound for the actual infinite sum.
(e) Explain exactly why M cannot be less than
Because our initial assumption has lead us to an absurd and contradictory assertion, we conclude that the initial
assumption must have been wrong. So e must have been a irrational number to begin with!
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