23666: HW 4 - Revision history

HelmutKnaust at 21:35, 12 March 2019

2019-03-12T21:35:57Z

HelmutKnaust at 21:27, 12 March 2019

2019-03-12T21:27:51Z

HelmutKnaust at 21:27, 12 March 2019

2019-03-12T21:27:38Z

HelmutKnaust: Created page with "'''Problem 16.''' Prove for all natural numbers $n\geq 5$: $2^n>n^2$. '''Problem 17.''' Let $n\in\mathbb{N}$. Conjecture a formula for the expression \[a_n=\frac{1}{1\cdot 2}..."

2019-03-12T21:27:17Z

Created page with "'''Problem 16.''' Prove for all natural numbers $n\geq 5$: $2^n>n^2$. '''Problem 17.''' Let $n\in\mathbb{N}$. Conjecture a formula for the expression \[a_n=\frac{1}{1\cdot 2}..."

New page

'''Problem 16.''' Prove for all natural numbers $n\geq 5$: $2^n>n^2$.

'''Problem 17.''' Let $n\in\mathbb{N}$. Conjecture a formula for the expression
\[a_n=\frac{1}{1\cdot 2}+\frac{1}{2\cdot 3}+\frac{1}{3\cdot 4}+\cdots +\frac{1}{n\cdot (n+1)}\] and prove your conjecture by induction.

'''Problem 18.''' Use Problem 15 and induction to show that ${\cal P}(A)$ has $2^n$ elements, when $A$ has $n$ elements.

← Older revision		Revision as of 21:27, 12 March 2019
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−	'''Problem 16.''' Prove for all natural numbers $n\geq 5$:~~\ \~~ $2^n>n^2$.	+	'''Problem 16.''' Prove for all natural numbers $n\geq 5$: $2^n>n^2$.

	'''Problem 17.''' Let $n\in\mathbb{N}$. Conjecture a formula for the expression		'''Problem 17.''' Let $n\in\mathbb{N}$. Conjecture a formula for the expression

← Older revision		Revision as of 21:27, 12 March 2019
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−	'''Problem 16.''' Prove for all natural numbers $n\geq 5$: $2^n>n^2$.	+	'''Problem 16.''' Prove for all natural numbers $n\geq 5$:\ \ $2^n>n^2$.

	'''Problem 17.''' Let $n\in\mathbb{N}$. Conjecture a formula for the expression		'''Problem 17.''' Let $n\in\mathbb{N}$. Conjecture a formula for the expression

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-'''Problem 16.''' Prove for all natural numbers $n\geq 5$:   $2^n>n^2$.
+'''Problem 16.''' Prove for all natural numbers $n\geq 5$:$\ \ \ \ 2^n>n^2$.
 '''Problem 17.''' Let $n\in\mathbb{N}$. Conjecture a formula for the expression
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 '''Problem 18.''' Use Problem 15 and induction to show that ${\cal P}(A)$ has $2^n$ elements, when $A$ has $n$ elements.