求級數的和 我要詳細算式 謝謝 1乘100+2乘99+、、、、+99乘2+100乘1?
回答 (2)
2016-03-20 10:58 am
✔ 最佳答案
Sol1*100+2*99+3*98+…+99*2+100*1
=Σ(k=1 to 100)_k*(100－k)
=Σ(k=1 to 100)_100k－k^2
=100Σ(k=1 to 100)k－Σ(k=1 to 100)_k^2
=100*100*101/2－100*101*201/6
=166650
2016-03-21 4:52 am
1*100+2*99+3*98+…+99*2+100*1
=Σ(k=1 to 100)_k*(100－k)
=Σ(k=1 to 100)_100k－k^2
=100Σ(k=1 to 100)k－Σ(k=1 to 100)_k^2
=100*100*101/2－100*101*201/6
=166650
=Σ(k=1 to 100)_k*(100－k)
=Σ(k=1 to 100)_100k－k^2
=100Σ(k=1 to 100)k－Σ(k=1 to 100)_k^2
=100*100*101/2－100*101*201/6
=166650
收錄日期: 2021-04-18 14:39:29
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20160320024548AAzXMSZ