document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1135125>Question 1135125</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write the sum using summation notation, assuming the suggested pattern continues. <BR>\n" );
document.write( "100 + 121 + 144 + 169 + ... + n2 + ... (2 points)<BR>\n" );
document.write( "choices are below<BR>\n" );
document.write( "	<BR>\n" );
document.write( "summation of n squared from n equals eleven to infinity<BR>\n" );
document.write( " 	<BR>\n" );
document.write( "summation of n minus one squared from n equals ten to infinity<BR>\n" );
document.write( " 	<BR>\n" );
document.write( "summation of n squared from n equals ten to infinity<BR>\n" );
document.write( " 	<BR>\n" );
document.write( "summation of n plus one squared from n equals ten to infinity<BR>\n" );
document.write( " </SPAN>\n" );
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document.write( "The answer choices are all very similar, showing the summation of squares going to infinity.  Which of the choices makes the first term of the sequence equal to 100 (=10 squared)?<br><BR>\n" );
document.write( "(1) summation of n squared from n equals eleven to infinity<BR>\n" );
document.write( "In the summation of (n squared) with 11 as the initial value, the first term is 11^2<br><BR>\n" );
document.write( "(2) summation of n minus one squared from n equals ten to infinity<BR>\n" );
document.write( "In the summation of ((n-1) squared) with 10 as the initial value, the first term is (10-1)^2 = 9^2<br><BR>\n" );
document.write( "(3) summation of n squared from n equals ten to infinity<BR>\n" );
document.write( "In the summation of (n squared) with 10 as the initial value, the first term is 10^2<br><BR>\n" );
document.write( "(4) summation of n plus one squared from n equals ten to infinity<BR>\n" );
document.write( "In the summation of ((n+1) squared) with 10 as the initial value, the first term is (10+1)^2 = 11^2<br><BR>\n" );
document.write( "The correct summation is clearly choice 3.<br><BR>\n" );
document.write( "But you will very often see summations similar to the other choices; there might be a good reason, in a particular problem, to define the summation in a way that doesn't seem the easiest.  For example, another summation that produces the given sequence could be<br><BR>\n" );
document.write( "summation of (n+4) squared from n equals six to infinity<br><BR>\n" );
document.write( "or<br><BR>\n" );
document.write( "summation of (n+9) squared from n equals one to infinity<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );