Simple inquality for tail sums and probability

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Given $K>0$ how do I show that: $$ \sum_{n\geq0}P(T>n)\leq K \sum_{n\geq0}P(T>nK) $$

I have tried to write out the sums to get a feeling but still could not work out how to show this... Doesn't K need to be a non-negative integer?