Step 1:
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The statement is .
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Condition I:
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First show that, the above formula is true, when .
Left hand side .
Right hand side .
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The statement is true for .
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Condition 1 of the Principle of Mathematical Induction holds.
\Step 2:
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Condition II :
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Assume that holds for some
, and determine whether the formula then holds for
.
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Assume that, for some
........equation(1).
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Now we show that,
\for some
.
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Left hand side from equation(1)
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Thus, Condition II also holds.
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The statement is true for all natural numbers.
\Solution:
\The statement is true for all natural numbers.