document.write( "Question 1150587: a)Determine the differential coefficient with respect to the variable.
\n" ); document.write( " Y=(x+1)^3
\n" ); document.write( "b). find the value of 8+6+4+........+(-32)
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #771995 by ikleyn(52787) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "a)Determine $\"highlight%28cross%28the%29%29\"$ $\"highlight%28cross%28differential%29%29\"$ different $\"highlight%28cross%28coefficient%29%29\"$ coefficients with respect to the variable.
\n" ); document.write( " Y=(x+1)^3
\n" ); document.write( "b). find the value of 8+6+4+........+(-32)
\n" ); document.write( "~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "(a)  As everybody knows who studied Algebra,  (x+1)^3 = x^3 + 3x^2 + 3x + 1,\r\n" );
document.write( "\r\n" );
document.write( "     so the coefficients are  1, 3, 3, 1.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "(b)  After canceling \" + \" and \" - \" terms, you have the sum\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "         Sum = -2*(5+6+7+8+9+10+11+12+13+14+15+16),    (*)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     and it can be computed in several clicks.  The answer is  -252.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     Also, you may use the formula\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "        5+6+7+8+9+10+11+12+13+14+15+16 = (1+2+3+4+5+6+ . . . +16) - (1+2+3+4) =  -  = 136-10 = 126,\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     and then your sum (*) is  Sum = -2*126 = -252,  giving the same value.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );