Certain Limits can be evaluated by using a method known as limit as a sum. Transforming a limit question to integration makes it easy to solve. Sometimes, it is only possible way to solve a question. The method is explained in the image.

Note that above result is only true when limit is infinity. Also, integration not always go from 0 to 1. Again it depends on Limit. If summation is ending at 2x where x-> (infinity), integration is from 0 to 2. (Why so?). If you can't point out why, Mention in comments and I will answer.

However, lower limit is always zero given that summation starts from a finite value.

Since I don't know how to use Latex or how to insert image in middle of text, I am using image to explain it all. Can someone tell me how to write in Latex and insert images in between text.

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Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

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