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
    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.

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