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Principle of Mathematical Induction
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Prove the following statement by the principle of mathematical induction : \[\] $n^3-n$ is divisible by 6, for each natural number $n \geq 2$.
cbse
class11
ch4
mathematical-induction
exemplar
q9
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May 5, 2014
by
thanvigandhi_1
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0
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Prove the following statement by the principle of mathematical induction : \[\] $n(n^2+5)$ is divisible by 6, for each natural number $n$.
asked
May 5, 2014
by
thanvigandhi_1
cbse
class11
ch4
mathematical-induction
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q10
0
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0
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Prove the following statement by the principle of mathematical induction : \[\] $n^2 < 2^n$ for all natural numbers $n \geq 5$.
asked
May 5, 2014
by
thanvigandhi_1
cbse
class11
ch4
mathematical-induction
exemplar
q11
0
votes
0
answers
Prove the following statement by the principle of mathematical induction : \[\] $ \sqrt n <\large\frac{1}{\sqrt 1}$$+\large\frac{1}{\sqrt 2}$$+...+\large\frac{1}{\sqrt n}$, for all natural numbers $n \geq 2$.
asked
May 5, 2014
by
thanvigandhi_1
cbse
class11
ch4
mathematical-induction
exemplar
q13
0
votes
0
answers
Prove the following statement by the principle of mathematical induction : \[\] For any natural number $n$, $x^n-y^n$ is divisible by $x-y$, where $x$ and $y$ are any integers with $x \neq y$.
asked
May 5, 2014
by
thanvigandhi_1
cbse
class11
ch4
mathematical-induction
exemplar
q8
0
votes
0
answers
Prove the following statement by the principle of mathematical induction : \[\] For any natural number $n$, $7^{n}-2^n$ is divisible by 5.
asked
May 5, 2014
by
thanvigandhi_1
cbse
class11
ch4
mathematical-induction
exemplar
q7
0
votes
0
answers
Prove the following statement by the principle of mathematical induction : \[\] $n^{3}-7n+3$ is divisible by 3, for all natural numbers $n$.
asked
May 5, 2014
by
thanvigandhi_1
cbse
class11
ch4
mathematical-induction
exemplar
q5
0
votes
0
answers
A sequence $d_1, d_2, d_3...$ is defined by letting $d_1=2$ and $d_k=\large\frac{d_{k-1}}{k}$ for all natural numbers $k \geq 2$. Show that $d_n = \large\frac{2}{n!}$ for all $n \in N$ by using principle of mathematical induction.
asked
May 6, 2014
by
thanvigandhi_1
cbse
class11
ch4
mathematical-induction
exemplar
q19
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