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NCERT Class 11- Math՚s: Chapter – 4 Principle of Mathematical Induction Part 3
Question 8:
Prove by induction that for all natural number
Answer:
Consider
We observe that
is true, since
Assume that is true for some natural numbers , i.e.. ,
Now, to prove that is true, we have
Thus is true whenever is true.
Hence, by the Principle of Mathematical Induction is true for all natural number .
Question 9:
Prove by the Principle of Mathematical Induction that
for all natural numbers n.
Answer:
Note that is true, since
Assume that is true for some natural number , i.e.. ,
To prove is true, we have
Thus is true, whenever is true. Therefore, by the Principle of Mathematical Induction, is true for all natural number n.