For each t $ \in R$, let [t] be the greatest integer less than or equal to t. Then $\mathop {\lim }\limits_{x \to {0^ + }} x\left( {\left[ {{1 \over x}} \right] + \left[ {{2 \over x}} \right] + ..... + \left[ {{{15} \over x}} \right]} \right)$

Question

For each t $ \in R$, let [t] be the greatest integer less than or equal to t.

Then $\mathop {\lim }\limits_{x \to {0^ + }} x\left( {\left[ {{1 \over x}} \right] + \left[ {{2 \over x}} \right] + ..... + \left[ {{{15} \over x}} \right]} \right)$

does not exist in R

is equal to 0

is equal to 15

is equal to 120

Solution

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