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.
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![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.](/uploads/image/z/5157126-54-6.jpg?t=%E5%B7%B2%E7%9F%A5%EF%BC%9A6%2F%28%28n%2B1%29%28n%2B2%29%28n%2B3%29%28n%2B3%29%29%3D%28a%2F%28n%2B1%29%29%2B%28b%2F%28n%2B2%29%29%28c%2F%28n%2B3%29%29%28d%2F%28n%2B4%29%29%E5%85%B6%E4%B8%ADa%2Cb%2Cc%2Cd%E6%98%AF%E5%B8%B8%E6%95%B0%2C%E5%88%99a%2B2b%2B3c%2B4d%E7%9A%84%E5%80%BC%E4%B8%BA___________.%E8%B0%A2.)
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