[Toán 8] Tính giá trị

K

key_bimat

T

transformers123

Để ý:

a+b=a2b2a+b=a^2-b^2 với a=b+1a=b+1a,bNa, b \in N

Áp dụng:

B=3(1.2)2+5(2.3)2+7(3.4)2+...+4029(2014.2015)2B=\dfrac{3}{(1.2)^2}+\dfrac{5}{(2.3)^2}+\dfrac{7}{(3.4)^2}+...+\dfrac{4029}{(2014.2015)^2}

    B=2212(1.2)2+3222(2.3)2+4232(3.4)2+...+2015220142(2014.2015)2\iff B=\dfrac{2^2-1^2}{(1.2)^2}+\dfrac{3^2-2^2}{(2.3)^2}+\dfrac{4^2-3^2}{(3.4)^2}+...+\dfrac{2015^2-2014^2}{(2014.2015)^2}

    B=2212.221212.22+3222.322222.32+...+2015220142.201522014220142.20152\iff B=\dfrac{2^2}{1^2.2^2}-\dfrac{1^2}{1^2.2^2}+\dfrac{3^2}{2^2.3^2}-\dfrac{2^2}{2^2.3^2}+...+\dfrac{2015^2}{2014^2.2015^2}-\dfrac{2014^2}{2014^2.2015^2}


    B=1122+122132+...+120142120152\iff B=1-\dfrac{1}{2^2}+\dfrac{1}{2^2 }-\dfrac{1}{3^2}+...+\dfrac{1}{2014^2}-\dfrac{1}{2015^2}

    B=1120152\iff B=1-\dfrac{1}{2015^2}

    B=40602244060225\iff B=\dfrac{4060224}{4060225}

Bến dưới có nút "Đúng", có gì bạn bấm vào giùm =))
 
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