数列求和公式(n-4)(n-3)(n-2)(n-1)nb^5 +5X(n-3)(n-2)(n-1)nb^4 +5X4X(

x1(n) =(n-4)(n-3)(n-2)(n-1)nb^5
= [b^5/6][ (n-4)(n-3)(n-2)(n-1)n(n+1) - (n-5)(n-4)(n-3)(n-2)(n-1)n]
S1(n)= x1(1)+x1(2)+...+x1(n)
= [b^5/6].(n-4)(n-3)(n-2)(n-1)n(n+1)
x2(n) = 5(n-3)(n-2)(n-1)nb^4
= b^4[(n-3)(n-2)(n-1)n(n+1) -(n-4)(n-3)(n-2)(n-1)n ]
S2(n)= x2(1)+x2(2)+...+x2(n)
=b^4.(n-3)(n-2)(n-1)n(n+1)
x3(n)=(5)(4)(n-2)(n-1)nb^3
= 5b^4 .[(n-2)(n-1)n(n+1) -(n-3)(n-2)(n-1)n]
S3(n)= x3(1)+x3(2)+...+x3(n)
=5b^4 .(n-2)(n-1)n(n+1)
x4(n)= (5)(4)(3)(n-1)nb^2
= 20b^2[ (n-1)n(n+1) - (n-2)(n-1)n]
S4(n)= x4(1)+x4(2)+...+x4(n)
=20b^2.(n-1)n(n+1)
x5(n) =(5)(4)(3)(2)nb
=60b[ n(n+1) -(n-1)n]
S5(n)= x5(1)+x5(2)+...+x5(n)
=60b.n(n+1)
x6(n)= (5)(4)(3)(2)(1) = 120
S6(n)= x6(1)+x6(2)+...+x6(n) = 120n
(n-4)(n-3)(n-2)(n-1)nb^5 +
5X(n-3)(n-2)(n-1)nb^4 +
5X4X(n-2)(n-1)nb^3 +
5X4X3X(n-1)nb^2 +
5X4X3X2Xnb^1 +
5X4X3X2X1
= x1(n)+x2(n)+x3(n)+x4(n)+x5(n)+x6(n)
sum =S1(n)+S2(n)+S3(n)+S4(n)+S5(n)+S6(n)
= [b^5/6].(n-4)(n-3)(n-2)(n-1)n(n+1) + b^4.(n-3)(n-2)(n-1)n(n+1)
+ 5b^4 .(n-2)(n-1)n(n+1) + 20b^2.(n-1)n(n+1) +60b.n(n+1) +120n