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

Name: Transform the following summation by making the change of variable i = k + 1: \[\sum _ { k = 0 } ^ { n } \frac { k ^ { 2 } } { k + n }\]
Brand: Quizplus
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Question

Quizplus · Accepted Answer

The Answer is When

k = 0 , i = 0 + 1 = 1

. When

k = n , i = n + 1

. Since

i = k + 1

, then

k = i - 1

. So

\frac { k ^ { 2 } } { k + n } = \frac { ( i - 1 ) ^ { 2 } } { i - 1 + n } .

Therefore,

\sum _ { k = 0 } ^ { n } \frac { k ^ { 2 } } { k + n } = \sum _ { i = 1 } ^ { n + 1 } \frac { ( i - 1 ) ^ { 2 } } { i - 1 + n }

Transform the Following Summation by Making the Change of Variable ∑k=0nk2k+n\sum _ { k = 0 } ^ { n } \frac { k ^ { 2 } } { k + n }k=0∑n​k+nk2​

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