Concept explainers
Use the following steps to show that the sequence
has a limit. (The value of the limit is denoted by γ and is called Euler’s constant.)
- (a) Draw a picture like Figure 6 with f(x) = 1/x and interpret tn as an area [or use (5)] to show that tn > 0 for all n.
- (b) Interpret
as a difference of areas to show that tn − tn+1 > 0. Therefore {tn} is a decreasing sequence.
- (c) Use the Monotonic Sequence Theorem to show that {tn} is convergent.
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Bundle: Multivariable Calculus, 8th + WebAssign Printed Access Card for Stewart's Calculus, 8th Edition, Single-Term
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