Question

[Vũ Huy nhật]

Giá trị biểu thức 4/3*5+4/5*7+4/7*9+.....+4/97*99+4/99*101/

Answer 1

[Nguyễn Đức Trí]

\(A=\dfrac{4}{3x5}+\dfrac{4}{5x7}+\dfrac{4}{7x9}+...+\dfrac{4}{97x99}+\dfrac{4}{99x101}\)

\(A=4x\left(\dfrac{1}{3x5}+\dfrac{1}{5x7}+\dfrac{1}{7x9}+...+\dfrac{1}{97x99}+\dfrac{1}{99x101}\right)\)

\(A=4x\left[\dfrac{1}{2}x\left(\dfrac{1}{3}-\dfrac{1}{5}\right)+\dfrac{1}{2}x\left(\dfrac{1}{5}-\dfrac{1}{7}\right)+\dfrac{1}{2}x\left(\dfrac{1}{7}-\dfrac{1}{9}\right)+...+\dfrac{1}{2}x\left(\dfrac{1}{97}-\dfrac{1}{99}\right)+\dfrac{1}{2}x\left(\dfrac{1}{99}-\dfrac{1}{101}\right)\right]\)

\(A=4x\dfrac{1}{2}x\left[\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+...+\dfrac{1}{97}-\dfrac{1}{99}+\dfrac{1}{99}-\dfrac{1}{101}\right]\)

\(A=2x\left(\dfrac{1}{3}-\dfrac{1}{101}\right)=2x\dfrac{98}{303}=\dfrac{916}{303}\)

Answer 2

[Vũ Huy nhật]

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