# Lim n tends to infinty [{(1^2+2^2+3^2+...n^2)(1^3+2^3+3^3+...n^3)}/(1^6+2^6+3^6+...n^6)]=??

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We know that

So,

Solving this, we get

Thus,

Use a similar process to find that

Then, the original problem becomes

See the other solution I posted for a method involving integration but is considerably easier.

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#### Explanation

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Describe your changes (optional) 200

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#### Explanation:

As

See the other solution I posted for an approach that does not resort to integration.

Describe your changes (optional) 200