a. Plot the series below and estimate the area using left and right rectangles to show that the partial sums of the harmonic series satisfy the inequalities shown below. n+1 T In(n+1)= b. There is absolutely no empirical evidence for the divergence of the harmonic series even though the series diverges. The partial sums just grow too slowly. To show this, suppose you had started with s, = 1 the day the universe was formed, 13 billion years ago, and added a new term every second. About how large would the partial sum s, be today, assuming a 365-day year? a. Ploty = = and estimate the area using right rectangles. Choose the correct plot below. OA 0 1 2 3 n •So dxss, s1+ n nt dx=1+ Inn 0 1 23 n-1 n G OC. 0 123 n n
a. Plot the series below and estimate the area using left and right rectangles to show that the partial sums of the harmonic series satisfy the inequalities shown below. n+1 T In(n+1)= b. There is absolutely no empirical evidence for the divergence of the harmonic series even though the series diverges. The partial sums just grow too slowly. To show this, suppose you had started with s, = 1 the day the universe was formed, 13 billion years ago, and added a new term every second. About how large would the partial sum s, be today, assuming a 365-day year? a. Ploty = = and estimate the area using right rectangles. Choose the correct plot below. OA 0 1 2 3 n •So dxss, s1+ n nt dx=1+ Inn 0 1 23 n-1 n G OC. 0 123 n n
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:9.3.49-T
a. Plot the series below and estimate the area using left and right rectangles to show that the partial sums of the harmonic series satisfy the inequalities shown below.
n+1
S
In (n+1)=
dxss, s1+
+ S²/dx=1
OA.
b. There is absolutely no empirical evidence for the divergence of the harmonic series even though the series diverges. The partial sums just grow too slowly. To show this, suppose you had started with s, = 1 the day the
universe was formed, 13 billion years ago, and added a new term every second. About how large would the partial sum s, be today, assuming a 365-day year?
a. Ploty and estimate the area using right rectangles. Choose the correct plot below.
n+
-dx=1+ Inn
Q
Q
n-1 n
O C.
23
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