How do you find the sum of the series #\sum _ { k = 1} ^ { 4} ( - 1) ^ { k } ( k ^ { 2} + 1)#?

1 Answer
Truong-Son N.
Dec 28, 2016

Manually? It's only to #k = 4#, so there are only four terms.

#color(blue)(sum _ (k = 1)^4 (-1)^k (k^2 + 1))#

#= (-1)^1(1^2 + 1) + (-1)^2(2^2 + 1) + (-1)^3(3^2 + 1) + (-1)^4(4^2 + 1)#

#= -(1 + 1) + (4 + 1) - (9 + 1) + (16 + 1)#

#= -2 + 5 - 10 + 17#

#= color(blue)(10)#

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