Transform the Following Summation by Making the Change of Variable $$\sum _ { k = 0 } ^ { n } \frac { k ^ { 2 } } { k + n }$$

question 28

Essay

Transform the following summation by making the change of variable i = k + 1: $$\sum _ { k = 0 } ^ { n } \frac { k ^ { 2 } } { k + n }$$

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Definitions:

Pathological Fear

An intense, irrational fear of a specific object, situation, or activity that is disproportionate to the actual threat or danger it poses.

Vivid Scenes

Vivid scenes refer to highly detailed and clear images or descriptions, often evoking strong mental or emotional responses.

Aversion Therapy

A form of psychological treatment where an undesirable behavior is paired with an unpleasant stimulus to reduce the behavior's occurrence.

Negative Reinforcement

A process in behavior analysis where the removal of an unpleasant stimulus strengthens a behavior, increasing the probability of its occurrence.