is equal to :

Question

is equal to :

Canvas Classes · Accepted Answer

🧠 Reading the Question — Expand the Sum, Use Leading-Order Asymptotics

The numerator is . Expand and split:

For large , leading-order:

- .
- .
- .

Numerator .

Denominator .

Ratio: .

🗺️ Working It Out

Numerator: . Expand .

Sum:

Using :

For large , leading-order:

- .
-  (sub-leading).
- .

So numerator .

Denominator:  at leading order.

Ratio:

⚡ The Smart Move

Memorize the leading-order behavior of standard sums:

- , , .

(General:  — looks like an integral approximation.)

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