Simple series

Task number: 2899

Compute the following limits.

  • Variant 1

    \(\displaystyle \lim_{n\to\infty} \frac{1+2+…+n}{n^2}\)

  • Variant 2

    \(\displaystyle \lim_{n\to\infty} \frac{1^2+2^2+…+n^2}{n^3}\)

  • Variant 3

    \(\displaystyle \lim_{n\to\infty}\left(\frac1{2}+\frac1{3}+\frac1{2^2}+\frac1{3^2}+\frac1{2^3}+\frac1{3^3}+…+\frac1{2^n}+\frac1{3^n}\right) \)

Difficulty level: Easy task (using definitions and simple reasoning)
Routine calculation training
Cs translation
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