1x2+2x3+3x4+...+n(n+1)=? 1x2x3+2x3x4+3x4x5+...+n(n+1)(n+2)=?

2025-01-04 02:44:09
推荐回答(3个)
回答1:

(1*1+1)+(2*2+2).......=(1*1+2*2+3*3......+N*N)+(1+2+3+4+...+N)=
同理,第二题乘出来:(1*1*1+2*2*2+3*3*3+......n*n*n)+3(1*1+2*2...+n*n)+2(1+2+3+4+..+n)=

回答2:

n(n+1)(n+2)/3
n(n+1)(n+2)(n+3)/4
......
定义:
n(n+1)(n+2)...(n+k)=[n]^k
则:
∑(i=1 to n)[n]^k=[n]^(k+1)/(k+1)=n(n+1)...(n+k+1)/(k+1)

回答3:

数列求和