請問各位大大，這題該怎麼解?
回答 (2)
2018-03-22 2:16 pm
✔ 最佳答案
Sol1+(1+2)+(1+2+3)+…+(1+2+3+…+n)
=(1*2)/2+(2*3)/2+(3*4)/2+…+n(n+1)/2
=(1/2)*Σ(k=1 to n)_k(k+1)
=(1/2) Σ(k=1 to n)_k^2+(1/2) Σ(k=1 to n)_k
=n(n+1)(2n+1)/12+n(n+1)/4
=[n(n+1)/12]*[(2n+1)+3]
=n(n+1)(n+2)/6
2018-03-22 2:25 pm
1+(1+2)+(1+2+3)+···+(1+2+3+···+n)
= (1×2 + 2×3 + 3×4 +...+ n(n+1))/2
= (1×2(3-0) + 2×3(4-1) + 3×4(5-2) +...
+ n(n+1)(n+2 - (n-1)) )/6
= (-0×1×2+1×2×3 - 1×2×3+2×3×4
- 2×3×4+3×4×5 -...+ n(n+1)(n+2))/6
= n(n+1)(n+2)/6
= (1×2 + 2×3 + 3×4 +...+ n(n+1))/2
= (1×2(3-0) + 2×3(4-1) + 3×4(5-2) +...
+ n(n+1)(n+2 - (n-1)) )/6
= (-0×1×2+1×2×3 - 1×2×3+2×3×4
- 2×3×4+3×4×5 -...+ n(n+1)(n+2))/6
= n(n+1)(n+2)/6
收錄日期: 2021-04-11 21:46:28
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20180321144553AAXohLd