Find the sum.
$\sum _ { k = 1 } ^ { 3 } \frac { 1 } { k ^ { 2 } + 5 }$

Question

Quizplus · Accepted Answer

The sum can be calculated by plugging in the values of $k$ from 1 to 3 into the given formula and adding the results:$$\sum _ { k = 1 } ^ { 3 } \frac { 1 } { k ^ { 2 } + 5 } = \frac { 1 } { 1 ^ { 2 } + 5 } + \frac { 1 } { 2 ^ { 2 } + 5 } + \frac { 1 } { 3 ^ { 2 } + 5 } = \frac { 1 } { 6 } + \frac { 1 } { 9 } + \frac { 1 } { 14 } = \frac { 7 } { 42 } + \frac { 14 } { 126 } + \frac { 9 } { 126 } = \frac { 22 } { 63 }.$$

Find the Sum ∑k=131k2+5\sum _ { k = 1 } ^ { 3 } \frac { 1 } { k ^ { 2 } + 5 }∑k=13​k2+51​

Find the Sum $\sum _ { k = 1 } ^ { 3 } \frac { 1 } { k ^ { 2 } + 5 }$