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Series S = sin0.2 rad

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A transcendental irrational number
S = sin0.2 rad
can be represented by the infinite series
S = sum (0 to infinity) of (-1)^n/[5^(2n+1) . (2n+1)!]
Let its partial sum be
SN = sum (0 to N) of (-1)^n/[5^(2n+1) . (2n+1)!]

a) Use the Ratio test to show the series converges absolutely.
b) Write down explicitly and compute the second (S2) partial sums.
Hint: in this case, S2 has three terms (using n = 0, 1, 2)
S2 =
c) Compute the theoretical error bound of the approximation S ~ S2
d) Use your computer or calculator to compute the proxy for exact value of sin 0.2. Observe the theoretical error bound holds for S2.
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Solution provided by:
J Pye, MSc
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  • MSc, California State Polytechnic University, Pomona
  • MBA, University of California, Riverside
  • BSc, California State Polytechnic University, Pomona
  • BSc, California State Polytechnic University, Pomona
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