USING MATHEMATICAL INDUCTION P(n)=1+22+2n+........+2n= 2n+1 - 1
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* I think the question is wrong. The statement will be such as
Let be a statement such that
Then is true for as
Now we show that the statement is true for smallest natural number .
Next we have to show for any , if holds, then also holds.
Assume that for , is true. .......(1)
Now we have to prove that is true.
Then [using (1)]
Therefore the statement holds true.
Hence by the principle of mathematical induction the given statement is true for all .