Write the sum (65 + 6) + (66 + 6) + (67 + 6) + (68 + 6) in summation notation in terms of k. (Use symbolic notation and fractions where needed.) 8 Σ k=5

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A: Topic:- application of derivatives and calculus

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A: we wil find the required.

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A: Recall the formula:

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A: Since you have posted multiple questions i can do first question as per our company guidelines…

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A: Given f( x ) = x2 + 1   ,  x &lt; 0          = | 1 - x |  ,   0 ≤ x &lt; 2         = x - 1   ,   x…