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According to the method of mathematical induction, one has to prove that statement
1) is correct for the initial value (in this task it is n=1)
2) assuming that the statement is valid for arbitrary n, prove its validity for (n+1).
Executing these steps, we obtain:
1) n = 1:
statement is proved.
2) assuming that
is correct, let us check it for (n+1) case:
Simplifying the left-hand side of the expression, one can derive:
which coincides with the right-hand side of the assumption.
By the method of mathematical induction the statement is true for all natural values of n.