document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=67665>Question 67665</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0669431621/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I am working with recursive functions.  I do not understand the examples given in the book. <BR>\n" );
document.write( "Example 1 is evaluating a recursive function. Use the following defintion to find the value of f(4).<BR>\n" );
document.write( "f(1)=3  and f(n)= f(n-1) + n<BR>\n" );
document.write( "solution:<BR>\n" );
document.write( "f(1)=3<BR>\n" );
document.write( "f(2)= f(1)+2=3+2=5   This is where I get lost. <BR>\n" );
document.write( "f(3)=f(2)+3=5+3=8<BR>\n" );
document.write( "f(4)=f(3)+4=8+4=12\r<BR>\n" );
document.write( "\n" );
document.write( "I understand factorals but this I do not understand.  Also is there a website that would guide me slower through the recursive functions?\r<BR>\n" );
document.write( "\n" );
document.write( "Thank you<BR>\n" );
document.write( "Kate </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #48140 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=48140\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use the following defintion to find the value of f(4).<BR>\n" );
document.write( "f(1)=3 and <BR>\n" );
document.write( "f(n)= f(n-1) + n<BR>\n" );
document.write( "You are given a starting point f(1)=3<BR>\n" );
document.write( "You are given a rule for generating the next number in the sequence:<BR>\n" );
document.write( "f(n) means any number of the sequence.<BR>\n" );
document.write( "f(n-1) means the number just before the one you are generating<BR>\n" );
document.write( "or the last one you generated.<BR>\n" );
document.write( "n is the number of the sequence you are generating.\r<BR>\n" );
document.write( "\n" );
document.write( "solution:<BR>\n" );
document.write( "f(1)=3<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "f(2)= f(1)+2 because f(1) comes just before f(2)<BR>\n" );
document.write( "then you add 2 because that is the number of sequence element.<BR>\n" );
document.write( "Since you were told f(1)=3, that is the 1st term below.<BR>\n" );
document.write( "=3+2<BR>\n" );
document.write( "=5 <BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "Now you go through the same process to generate f(3) <BR>\n" );
document.write( "f(3)=f(2)+3<BR>\n" );
document.write( "=5+3<BR>\n" );
document.write( "=8<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "f(4)=f(3)+4<BR>\n" );
document.write( "=8+4<BR>\n" );
document.write( "=12<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "Do you see that f(5)would be f(4)+5<BR>\n" );
document.write( "=12+5<BR>\n" );
document.write( "=17 <BR>\n" );
document.write( "---------<BR>\n" );
document.write( "Do you see that this process could go on forever?<BR>\n" );
document.write( "That's what makes it recursive.<BR>\n" );
document.write( "-----------<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );