Stack life

Let $$S$$ be a stack of size greater than $$1$$. Starting from an empty stack, suppose we push the first $$n$$ natural numbers in sequence and then perform $$n$$ pop operations. For $$1\leq x\leq n$$ the stack life of $$x$$ is defined as the time taken from the end of push(x) to the start of the pop operation that removes $$x$$ from $$S$$. What of the following is the correct representation for the average stack life of $$x$$?

Details and Assumptions

• $$k$$ is the number of seconds required to pop and push an item
• $$l$$ is the number of seconds elapsed between each successive operations.
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