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\(\text{Let $f(n)$ be the base-10 logarithm of the sum of the elements of the $n$th row in Pascal's triangle. Express $\frac{f(n)}{\log_{10} 2}$ in terms of $n$. Recall that Pascal's triangle begins}\)

 Sep 7, 2019
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\(\text{Let $f(n)$ be the base-10 logarithm of the sum of the elements of the $n$th row in Pascal's triangle.$\\$Express $\frac{f(n)}{\log_{10} 2}$ in terms of $n$. Recall that Pascal's triangle begins}\)

 

 

\(\begin{array}{|rcll|} \hline f(n) &=& \log_{10} 2^n \\ \mathbf{f(n)} &=& \mathbf{n\log_{10} 2} \\ \hline \end{array} \)

 

\(\begin{array}{|rcll|} \hline \dfrac{f(n)}{\log_{10} 2} &=& \dfrac{n\log_{10} 2}{\log_{10} 2} \\\\ \mathbf{\dfrac{f(n)}{\log_{10} 2} } &=& \mathbf{n} \\ \hline \end{array}\)

 

laugh

 Sep 7, 2019

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