Write a program to solve the following problem- Euler's number e is used as the base of natural logarithms. It may be approximated using the following formula: where n is sufficiently large. Write a program that approximates e using a loop that terminates when the difference between the two successive values of e is less than 0.0000001.

C Programming Language Loop control in C Language (Article) Loop control in C Language (Program)

7441

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Program:

<span class="com">#include</span><span class="pln"> </span><span class="str">&lt;stdio.h&gt;</span><span class="pln">
</span><span class="kwd">int</span><span class="pln"> main</span><span class="pun">()</span><span class="pln">
</span><span class="pun">{</span><span class="pln">
	</span><span class="kwd">double</span><span class="pln"> term </span><span class="pun">=</span><span class="pln"> </span><span class="lit">1.0</span><span class="pun">;</span><span class="pln">
	</span><span class="kwd">double</span><span class="pln"> sum </span><span class="pun">=</span><span class="pln"> </span><span class="lit">1.0</span><span class="pun">;</span><span class="pln">
	</span><span class="kwd">int</span><span class="pln"> n </span><span class="pun">=</span><span class="pln"> </span><span class="lit">0</span><span class="pun">;</span><span class="pln">
	</span><span class="kwd">while</span><span class="pln"> </span><span class="pun">(</span><span class="pln">term </span><span class="pun">&gt;=</span><span class="pln"> </span><span class="lit">0.0000001</span><span class="pun">)</span><span class="pln">
	</span><span class="pun">{</span><span class="pln">
		n</span><span class="pun">++;</span><span class="pln">
		term </span><span class="pun">=</span><span class="pln"> term</span><span class="pun">/</span><span class="pln">n</span><span class="pun">;</span><span class="pln">
		sum </span><span class="pun">=</span><span class="pln"> sum </span><span class="pun">+</span><span class="pln"> term</span><span class="pun">;</span><span class="pln">
	</span><span class="pun">}</span><span class="pln">
	printf</span><span class="pun">(</span><span class="str">"\n Approximate value of e is: %lf "</span><span class="pun">,</span><span class="pln">sum</span><span class="pun">);</span><span class="pln">
	
	getch</span><span class="pun">();</span><span class="pln">
	</span><span class="kwd">return</span><span class="pln"> </span><span class="lit">0</span><span class="pun">;</span><span class="pln">
</span><span class="pun">}</span>

Output:

 Approximate value of e is: 2.718282

Explanation:

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