Test_2_Study_Outline.ipynb

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    "# Test II \n",
    "\n",
    "## Study Plan \n",
    "\n",
    "<p class='lead'>This is an outline of all the topics and sub-topics, theorems, concepts, and tests, etc. which I'll need to know in order to pass __Test II__ with a good grade.</p>"
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    "___\n",
    "\n",
    "<ol class='roman outline'>\n",
    "    <li>\n",
    "        <h3>Improper Integrals</h3>\n",
    "        <span class='section'>7.8</span>\n",
    "    </li>\n",
    "    <li>\n",
    "        <h3>Sequences</h3>\n",
    "        <span class='section'>11.1</span>\n",
    "        <ol class='alpha'>\n",
    "            <li>Limit of Function/Limit of Sequence Relationship Theorem</li>\n",
    "            <li>Infinite Limit of a Sequence</li>\n",
    "            <li>__Limit Laws for Sequences__</li>\n",
    "            <li>Squeeze Theorem for Sequences</li>\n",
    "            <li>Limit of Absolute Value of a Sequence</li>\n",
    "            <li>__Convergence of Sequences__</li>\n",
    "            <li>Upper Bounds of Sequences</li>\n",
    "            <li>Lower Bounds of Sequences</li>\n",
    "            <li>Monotonic Sequences</li>\n",
    "            <li>Bounded Monotonic Sequences Converge</li>\n",
    "        </ol>\n",
    "    </li>\n",
    "    <li>\n",
    "        <h3>Series</h3>\n",
    "        <span class='section'>11.2</span>\n",
    "        <ol class='alpha'>\n",
    "            <li>Definition of Series Convergence</li>\n",
    "            <li>Definition of Series Divergence</li>\n",
    "            <li>Definition of Partial Sums</li>\n",
    "            <ol class='roman-l'>\n",
    "                <li>__Nth Partial Sum__</li>\n",
    "                <li>__Sequence of Partial Sums__</li>\n",
    "            </ol>\n",
    "            <li>\n",
    "                Geometric Series\n",
    "                <ol class='roman-l'>\n",
    "                    <li>Common Ration</li>\n",
    "                    <li>Convergence of Geometric Series ( $|r| < 1$ )</li>\n",
    "                    <li>\n",
    "                        Formula for the Sum of a Geometric Series<br/>\n",
    "                        $\\sum_{n=1}^{\\infty} ar^{n-1} = \\frac{a}{1-r}$\n",
    "                    </li>\n",
    "                </ol>\n",
    "            </li>\n",
    "            <li>Harmonic Series</li>\n",
    "            <li>\n",
    "                __Nth Term Test__<br/>\n",
    "                $\\sum_{n=1}^{\\infty}a_n$ diverges if $\\lim_{n\\to\\infty}a_n \\ne 0$ or _fails to exist._\n",
    "            </li>\n",
    "            <li>Adding or Deleting Terms in a Series (doesn't alter convergence/divergence)</li>\n",
    "            <li>Can change __index start value__</li>\n",
    "            <li>__Limit Laws for Series__</li>\n",
    "        </ol>\n",
    "    </li>\n",
    "    <li>\n",
    "        <h3>Integral Test</h3>\n",
    "        <span class='section'>11.3</span>\n",
    "        <ol class='alpha'>\n",
    "            <li>Non-Decreasing Partial Sums<br/>(only converges if bounded from above)</li>\n",
    "            <li>__Integral Test Theorem__</li>\n",
    "            <li>\n",
    "                P-Series<br/>\n",
    "                <ol class='roman-l'>\n",
    "                    <li>Difference between _P-Series &amp; Geometric Series_\n",
    "                </ol>\n",
    "            </li>\n",
    "            <li>\n",
    "                __Estimating Sums of Series__<br/>\n",
    "                <ol class='roman-l'>\n",
    "                    <li>Estimating size of remainder</li>\n",
    "                    <li>Bounds for remainder in _Integral Test_</li>\n",
    "                    \n",
    "                </ol>\n",
    "            </li>\n",
    "            <li></li>\n",
    "            <li></li>\n",
    "            <li></li>\n",
    "            <li></li>\n",
    "        </ol>\n",
    "    </li>\n",
    "    <li>\n",
    "        <h3>Comparison Tests</h3>\n",
    "        <span class='section'>11.4</span>\n",
    "        <ol class='alpha'>\n",
    "            <li>__Comparison Test__</li>\n",
    "            <li>__Limit Comparison Test__</li>\n",
    "            <li>Estimating Sums with the Comparison &amp; Limit Comparison Tests</li>\n",
    "        </ol>\n",
    "    </li>\n",
    "    <li>\n",
    "        <h3>Alternating Series</h3>\n",
    "        <span class='section'>11.5</span>\n",
    "        <ol class='alpha'>\n",
    "            <li>Estimating Sums of Alternating Series<br/>\n",
    "                <ol class='roman-l'>\n",
    "                    <li>Alternating Series Estimation Theorem</li>\n",
    "                    \n",
    "                </ol>\n",
    "            </li>\n",
    "            <li>__Alternating Series Test__</li>\n",
    "        </ol>\n",
    "    </li>\n",
    "    <li>\n",
    "        <h3>Ratio &amp; Root Tests</h3>\n",
    "        <span class='section'>11.6</span>\n",
    "        <ol class='alpha'>\n",
    "            <li>__Absolute Convergence__</li>\n",
    "            <li>__Conditional Convergence__</li>\n",
    "            <li>__Ratio Test__</li>\n",
    "            <li>_Root Test__</li>\n",
    "            <li>__Rearranging Series__</li>\n",
    "        </ol>\n",
    "    </li>\n",
    "    <li>\n",
    "        <h3>Series Testing Strategy</h3>\n",
    "        <span class='section'>11.7</span>\n",
    "        <ol class='alpha'>\n",
    "        </ol>\n",
    "    </li>\n",
    "</ol>"
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