document.write( "Question 28681: Conjecture a formula for the following sum 1(1!)+2(2!)+3(3!)+...+n(n!). \n" ); document.write( "

Algebra.Com's Answer #15637 by venugopalramana(3286) $\"\"$ $\"About$

You can put this solution on YOUR website!
Conjecture a formula for the following sum 1(1!)+2(2!)+3(3!)+...+n(n!).
\n" ); document.write( "CONSIDER THE EQN.
\n" ); document.write( "(N+1)!-N! = N!*(N+1-1)=N*N!
\n" ); document.write( "NOW PUT N=1,2,3.... ETC..TILL N IN THIS EQN.AND ADD UP.,WE GET
\n" ); document.write( "FOR N=1.......2!-1! = 1*1!
\n" ); document.write( "N=2...........3!-2! = 2*2!
\n" ); document.write( "N=3...........4!-3! = 3*3!
\n" ); document.write( "..........................ETC
\n" ); document.write( "N=N........(N+1)!-N!=N*N!
\n" ); document.write( "-----------------------------ADD ALL
\n" ); document.write( "...........(N+1)!-1!=1*1!+2*2!+3*3!+.........+N*N!
\n" ); document.write( "----------------------------------------------------- \n" ); document.write( "

\n" );