4 thoughts on “Tổng và tích (1)”

  1. Cach tiep can dep de nhat doi voi cac tong huu han hay cac tich huu han theo toi do la su dung dinh li sau:

    Dinh li. Cho day cac so a_1,a_2,...,a_n,a_{n+1}. Khi do
    a)\sum_{i=1}^n(a_{i+1}-a_i)=a_{n+1}-a_1.
    b) Neu co them tat ca cac so hang cua day khac khong thi \prod_{i=1}^n\dfrac{a_{i+1}}{a_i}=\dfrac{a_{n+1}}{a_1}.

    Chung minh. De! \Box

  2. Bai 5.([1])
    Tinh \sum_{k=1}^n\cos kx.
    Bai 6.([1])
    Tinh \sum_{k=0}^n\tan^{-1}\dfrac{1}{k^2+k+1}.
    Bai 7.([1])
    Chung minh rang \sum_{i=1}^n\dfrac{\sin ix}{\cos^i x}=\cot x-\dfrac{\cos (n+1)x}{\sin x\cos^n x} voi moi x\not = \dfrac{k\pi}{2},k\in\mathbb{Z}.
    Bai 8.([1])
    Chung minh rang \sum_{i=0}^{88}\dfrac{1}{\cos i^{0}\cos (i+1)^0}=\dfrac{\cos 1^{0}}{\sin^2 1^{0}}.

    Tai lieu tham khao:
    [1] Mathematical Olympiad Challenges, Titu Andreescu and Razvan Gelca, Birkhauser.

Leave a Reply

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

WordPress.com Logo

You are commenting using your WordPress.com 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 )

Google+ photo

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

Connecting to %s