Mathematics · Algebra

What is 1 / (1 + &sqrt;2) + 1 / (&sqrt;2 + &sqrt;3) + 1 / (&sqrt;3 + &sqrt;4) + ... + 1 / (&sqrt;2020 + &sqrt;2021) equal to?

Verified Solution4 OptionsUpdated: October 2026👁️1 View

1&sqrt;2021 - 1✓
2&sqrt;2020 + &sqrt;2021 - 1
3&sqrt;2021 + 1
4&sqrt;2020 + 1

Correct answer

&sqrt;2021 - 1

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What is 1 / (1 + &sqrt;2) + 1 / (&sqrt;2 + &sqrt;3) + 1 / (&sqrt;3 + &sqrt;4) + ... + 1 / (&sqrt;2020 + &sqrt;2021) equal to?

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What is 1 / (1 + &sqrt;2) + 1 / (&sqrt;2 + &sqrt;3) + 1 / (&sqrt;3 + &sqrt;4) + ... + 1 / (&sqrt;2020 + &sqrt;2021) equal to?

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