In 1795, Leonhard Euler proved that the sum of the following infinite series is equal to 72/6 1 1 + 22 1 1 Σ (1) 1+ k2 k=1 32 42 a). Use a for loop to sum the first twenty terms of the series and compare this partial sum with n²/6 (compute the relative error) b). Write a while loop that will determine how many terms must be summed to produce an approximation of T² /6 that is correct to 4 significant digits.

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In 1795, Leonhard Euler proved that the sum of the following
infinite series is equal to 72/6
1
1+
22
1
1
+
42
(1)
%3D
..
32
k=1
a). Use a for loop to sum the first twenty terms of the series and
compare this partial sum with a²/6 (compute the relative
error)
_2
b). Write a while loop that will determine how many terms must
be summed to produce an approximation of 72/6 that is
correct to 4 significant digits.
Transcribed Image Text:In 1795, Leonhard Euler proved that the sum of the following infinite series is equal to 72/6 1 1+ 22 1 1 + 42 (1) %3D .. 32 k=1 a). Use a for loop to sum the first twenty terms of the series and compare this partial sum with a²/6 (compute the relative error) _2 b). Write a while loop that will determine how many terms must be summed to produce an approximation of 72/6 that is correct to 4 significant digits.
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