1×3+2×4+3×5+…+(N-1)×(N+1)等于多少

2024-10-30 22:18:11
推荐回答(4个)
回答1:

1×3+2×4+3×5+4×6+......+(N-1)×(N+1)
=2²-1+3²-1+4²-1+.......+N²-1
=2²+3²+4²+.......+N²-(N-1)
前面有公式的

回答2:

1×3+2×4+3×5+......+(N-1)×(N+1)
=2²-1+3²-1+4²-1+.......+N²-1
=2²+3²+4²-1+.......+N²-(N-1)
=2²+3²+4²-1+.......+N²-N+1
=1²+2²+3²+4²-1+.......+N²-N
=N(N+1)(2N+1)/6-N

回答3:

1×3+2×4+3×5+…+(N-1)×(N+1)=(N/6)×(2N²+3N-5)=(N/6)(2N+5)(N-1)=N(2N+5)(N-1)/6

回答4:

1*2*3=1/4(1*2*3*(4-0)
2*3*4=1/4(2*3*4*(5-1)
.
n*(n+1)*(n+2)=1/4*n*(n+1)*(n+2)[n+3-(n-1)]
Sn=1*2*3+2*3*4+3*4*5+...+n*(n+1)*(n+2)
=1/4{1*2*3*(4-0)+2*3*4*(5-1)+3*4*5*(6-2)...+n*(n+1)*(n+2)[n+3-(n-1)]
=1/4{1*2*3*4+2*3*4*5-1*2*3*4+3*4*5*6-2*3*4*5+.+n*(n+1)(n+2)(n+3)-(n-1)*n(n+1)(n+2)} 原式= n*(n+1)*(n+2)*(n+3)/4