已知：6/((n+1)(n+2)(n+3)(n+3))=(a/(n+1))+(b/(n+2))(c/(n+3))(d/(n+4))其中a,b,c,d是常数,则a+2b+3c+4d的值为___________.谢.

已知：6/((n+1)(n+2)(n+3)(n+3))=(a/(n+1))+(b/(n+2))(c/(n+3))(d/(n+4))其中a,b,c,d是常数,则a+2b+3c+4d的值为___________.谢.
已知：
6/((n+1)(n+2)(n+3)(n+3))=(a/(n+1))+(b/(n+2))(c/(n+3))(d/(n+4))
其中a,b,c,d是常数,则a+2b+3c+4d的值为___________.
谢.

已知：6/((n+1)(n+2)(n+3)(n+3))=(a/(n+1))+(b/(n+2))(c/(n+3))(d/(n+4))其中a,b,c,d是常数,则a+2b+3c+4d的值为___________.谢.
6/[(n+1)(n+2)(n+3)(n+4)]
=6/{[(n+1)(n+4)][(n+2)(n+3)]}
=6/[(n的平方+5n+4)(n的平方+5n+6)
=3/(n的平方+5n+4) - 3/(n的平方+5n+6)
=3/[(n+1)(n+4)] - 3/[(n+2)(n+3)]
=[1/(n+1) - 1/(n+4)]-[3/(n+2) - 3/(n+3)]
=1/(n+1)+(-3)/(n+2)+3/(n+3)+(-1)/(n+4)
所以：a=1 b=-3 c=3 d=-1
所以：a+2b+3c+4d=1+2*(-3)+3*3+4*(-1)=0