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State recursion and its different types?

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The most basic tool used to express generating functions in closed form is the closed form expression for the geometric series, which is an expression of the form a+ar+ar2++arn. It can either be terminated or extended indefinitely. What are the restrictions for this geometric series?

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How do you apply Binary Search on 2D array supposed you have 2D array with integers sorted both horizontally and vertically. If you find any occurrence of the value you are looking for you return true else false. What is the complexity?
For example the 2D array could look like the following
1 4 5 6 2 5 7 9

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