Prove the following by the principle of mathematical induction:
Answer:
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Now substituting the from equation i)
Hence by the principle of mathematical induction
Answer:
… … … … … i)
Now substituting the from equation i)
Hence by the principle of mathematical induction
Answer:
… … … … … i)
Now substituting the from equation i)
Hence by the principle of mathematical induction
Answer:
… … … … … i)
Now substituting the from equation i)
Hence by the principle of mathematical induction
i.e., the sum of firs odd numbers is
Answer:
… … … … … i)
Now substituting the from equation i)
Hence by the principle of mathematical induction
Answer:
… … … … … i)
Hence by the principle of mathematical induction
Answer:
… … … … … i)
Hence by the principle of mathematical induction
Answer:
… … … … … i)
Answer:
… … … … … i)
Hence by the principle of mathematical induction
Answer:
… … … … … i)
Hence by the principle of mathematical induction
Answer:
… … … … … i)
Hence by the principle of mathematical induction
Answer:
… … … … … i)
Hence by the principle of mathematical induction
Answer:
… … … … … i)
Hence by the principle of mathematical induction
Answer:
… … … … … i)
Hence by the principle of mathematical induction
Answer:
… … … … … i)
Hence by the principle of mathematical induction
Answer:
… … … … … i)
Hence by the principle of mathematical induction
Answer:
… … … … … i)
Hence by the principle of mathematical induction
Answer:
… … … … … i)
Hence by the principle of mathematical induction
is divisible by for all
Answer:
is divisible by for all
which is divisible by 24
Hence
is divisible by for all
… … … … … i)
where
Hence by the principle of mathematical induction
is divisible by for all
is divisible by for all
Answer:
is divisible by for all
which is divisible by
Hence
is divisible by for all
… … … … … i)
where
Hence by the principle of mathematical induction
is divisible by for all
is divisible by for all
Answer:
is divisible by for all
which is divisible by
Hence
is divisible by for all
… … … … … i)
where
Hence by the principle of mathematical induction
is divisible by for all
is divisible by for all
Answer:
is divisible by for all
which is divisible by
Hence
is divisible by for all
… … … … … i)
where
Hence by the principle of mathematical induction
is divisible by for all
for all
Answer:
for all
RHS Therefore LHS = RHS
Hence
for all
Hence by the principle of mathematical induction
for all
is a multiple of for all
Answer:
is a multiple of for all
which is divisible by
Hence
is divisible by for all
… … … … … i)
where
Hence by the principle of mathematical induction
is a multiple of for all
is divisible by for all
Answer:
is divisible by for all
which is divisible by
Hence
is divisible by for all
… … … … … i)
where
Hence by the principle of mathematical induction
is divisible by for all