设(1+x)^3+(1+x)^4+(1+x)^5+...+(1+x)^50=a0+(a1)x+(a2)x^2+(a3)x^3+...+(a50)x^50则a3的值?
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![设(1+x)^3+(1+x)^4+(1+x)^5+...+(1+x)^50=a0+(a1)x+(a2)x^2+(a3)x^3+...+(a50)x^50则a3的值?](/uploads/image/z/5967557-53-7.jpg?t=%E8%AE%BE%281%2Bx%29%5E3%2B%281%2Bx%29%5E4%2B%281%2Bx%29%5E5%2B...%2B%281%2Bx%29%5E50%3Da0%2B%28a1%29x%2B%28a2%29x%5E2%2B%28a3%29x%5E3%2B...%2B%28a50%29x%5E50%E5%88%99a3%E7%9A%84%E5%80%BC%3F)
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设(1+x)^3+(1+x)^4+(1+x)^5+...+(1+x)^50=a0+(a1)x+(a2)x^2+(a3)x^3+...+(a50)x^50则a3的值?
设(1+x)^3+(1+x)^4+(1+x)^5+...+(1+x)^50=a0+(a1)x+(a2)x^2+(a3)x^3+...+(a50)x^50则a3的值?
设(1+x)^3+(1+x)^4+(1+x)^5+...+(1+x)^50=a0+(a1)x+(a2)x^2+(a3)x^3+...+(a50)x^50则a3的值?
a3=C(3,3)+C(3,4)+...+C(3,50)(C(x,y)表示x上y下)
a3=C(4,3)+C(3,3)+...+C(3,50)-C(4,3)=C(4,50)=230300
(有引理C(m,n)+C(m-1,n)=C(m,n+1),易证)