Sharedcheat_sheet.sagewsOpen in CoCalc
Author: Matt Thomas
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# This line makes the output nicely typeset %typeset_mode True
# Define a sequence a(n)=1/n
# Print a sequence [a(i) for i in [1..10]]
[1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9, 1/10]
# Define a series (sequence of partial sums) def s(k): return sum([a(i) for i in [1..k]])
# Print a sequence of partial sums [s(i) for i in [1..10]]
[1, 3/2, 11/6, 25/12, 137/60, 49/20, 363/140, 761/280, 7129/2520, 7381/2520]
# Plot a sequence L = [a(i) for i in [1..10]] list_plot(L, pointsize=50, color='green')
# Plot sequence of partial sums (i.e. partial sums in a series) S = [s(i) for i in [1..10]] list_plot(S, pointsize=50, color='red')
# Indefinite integral integral(1/x^2, x)
-1/x
# Definite integral from 4 to 5 integral(1/x^2, x, 4, 5)
120\displaystyle \frac{1}{20}
# Improper integral integral(1/x^2, x, 1, infinity)
1\displaystyle 1