How do you find the sum given #sum_(k=0)^4 1/(k^2+1)#?

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How do you find the sum given #sum_(k=0)^4 1/(k^2+1)#?

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Answer 1 · 2016-10-31T13:19:14

# sum_(k=0)^(k=4) 1/(k^2+1) = 158/85#

Explanation:

# sum_(k=0)^(k=4) 1/(k^2+1) = 1/(0^2+1) + 1/(1^2+1) + 1/(2^2+1) + 1/(3^2+1) + 1/(4^2+1)#
# :. sum_(k=0)^(k=4) 1/(k^2+1) = 1/(0+1) + 1/(1+1) + 1/(4+1) + 1/(9+1) + 1/(16+1)#
# :. sum_(k=0)^(k=4) 1/(k^2+1) = 1/1 + 1/2 + 1/5 + 1/10 + 1/17#
# :. sum_(k=0)^(k=4) 1/(k^2+1) = 158/85#

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How do you find the sum given #sum_(k=0)^4 1/(k^2+1)#?

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