Math 206 Homework

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{\Large Jibri Kea} \hfill
{\large Math 206, Section 2,}  %Delete one
\hfill  \today

I worked with:


\begin{enumerate}
\item  \textbf{Problem 6: Number Systems} Perform D3F02 (hex) + C34D (hex). State your answer in hexadecimal and decimal.


D3F02h + C34Dh

\[ D		 3		 F		 0		 2 		h\]

\[1101 +	0011 +	1111 +	0000 +	0010	b\]
\[ 13	+	 3 	 +	 15   +	 0	 +	 2		d\]
\[13*16^{4} + 3*16^{3}  +  15*16^{2}  + 0*16^{1}  + 2*16^{0}\]
\[851,968 + 12,288 + 3,840 + 0 + 2d\]
\[868,098d\]


\[C34Dh\]

\[1100+0011+0100+1101b\]
\[12+3+4+13d\]
\[12*16^{3}  +  3*16^{2}  + 4*16^{1}  + 13*16^{0}\]
\[49,152+768+64+13d\]
\[49,997d\]

\[D3F02h+C34Dh= 918,095d\]
\[11010011111100000010b\]
\[+1100001101001101b\]
\[11100000001001001111b\]
\[14+0+2+4+15h\]
\[E024Fh = 918,095d\]







\item \textbf{Problem 8: Number Systems} Convert 109 to base 7.


\[109 / 7 = 15 R4\]
\[15 / 7 = 2 R1\]

\[214_{7}\]
\[2*2^{2}*7^{1}+4*7^{0}\]
\[98+7+4 =109d=214_{7}\]



\item \textbf{Problem 19} Find a closed form.
\[1,4,7,10,13,16,19\]
\[a_{n} = c+dn+fn^{2}\]
\[a_{1} = c+d+f=1\]
\[a_{2} = c+2d+4f=4\]
\[a_{3} = c+3d+9f=7\]
\[c=-2\]
\[d=3\]
\[f=0\]
\[a_{n}=-2+3n\]



\item \textbf{Problem 19} Find a closed form.
\[-1,1,3,5,7,9,11\]
For n is greater than/equal to 0.
\[GUESS a_{n}=2_{n-1}\] 
\[n=0: True -1=0-1=-1\]
Assume for some n >= 1. a(k) = 2(k) - 1
\[=4n-2-2n+3=2n+1=2(n+1)-1\]




\end{enumerate}

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