Question: Use mathematical induction to prove that is a sequence of pair wise disjoint events in a sample space , where is a positive integer, then .
It is proved that .
It is given that that is a sequence of pair wise disjoint events in a sample space , here is a positive integer.
Principle of mathematical Induction states that “Let be a property of positive integers such that,
Basic Step: is true
Inductive Step: if is true, then is true
Then, is true for all positive integers.”
By using mathematical induction prove the result for
As are disjoint events
Applying the result in equation
Thus, the result is true for
Assume it is true for
Prove the result for
Use equation and in the above equation
It is true for
Here is a positive integer
Thus, it is proved that .
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