document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1122511>Question 1122511</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the sum of each of the following inifinite G.P's:<BR>\n" );
document.write( "(a) 1 + 1/3 + 1/9 + 1/27 + +...<BR>\n" );
document.write( "(b) 2/5 + 3/5^2 + 2/5^2 + 3/5^4... </SPAN>\n" );
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document.write( "Th infinite sum of a geometric progression with common ratio between -1 and 1 is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2F%281-r%29 ALIGN=MIDDLE  ALT=\"a%2F%281-r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "where a is the first term and r is the common ratio.<br><BR>\n" );
document.write( "(a) first term 1; common ratio 1/3.  Plug the numbers into the formula.<br><BR>\n" );
document.write( "(b) I will assume the third term is supposed to be 2/5^3 instead of 2/5^2....<br><BR>\n" );
document.write( "It's probably easiest to group the terms in pairs.  Then the first term is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F5+%2B+3%2F5%5E2+=+%2810%2B3%29%2F5%5E2+=+13%2F25 ALIGN=MIDDLE  ALT=\"2%2F5+%2B+3%2F5%5E2+=+%2810%2B3%29%2F5%5E2+=+13%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Grouping the terms in pairs like that then makes the common ratio between the paired terms 1/5^2 = 1/25.<br><BR>\n" );
document.write( "There are the first term and common ratio.  Again plug them into the formula. </SPAN>\n" );
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