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)
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.
What does this mean?
Step-by-step computations and explanations are shown for the questions.