Ngô Quốc Anh

August 28, 2007

Sử dụng Tích phân xác định tính tổng vô hạn

Filed under: Các Bài Tập Nhỏ — Ngô Quốc Anh @ 16:15

Đề bài: Chứng minh hệ thức


Lời giải:

More generally, let k be a natural number. Then

\sum_{m_{1},m_{2},\cdots, m_{n}\geq 1}\frac{1}{m_{1}\cdots m_{n}(m_{1}+m_{2}+\cdots+m_{n}+k)}=


We have that

S=\sum\frac{1}{m_{1}\cdots m_{n}}\int_{0}^{1}x^{m_{1}+\cdots+m_{n}+k-1}dx




When n=2 and k=2 we get that the sum equals



Leave a Comment »

No comments yet.

RSS feed for comments on this post. TrackBack URI

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Blog at

%d bloggers like this: