Question

cho đa thức f(x)=x(x+1)+(x+1)(x+2)+(x+2)(x+3)+..+(x+49)(x+50) tinh f(1)

Answer 1

\(f\left(x\right)=x\left(x+1\right)+\left(x+1\right)\left(x+2\right)+\left(x+2\right)\left(x+3\right)+...+\left(x+49\right)\left(x+50\right)\)

\(f\left(1\right)=1\left(1+1\right)+\left(1+1\right)\left(1+2\right)+\left(1+2\right)\left(1+3\right)+...+\left(1+49\right)\left(1+50\right)\)

\(f\left(1\right)=1.2+2.3+3.4+...+50.51\)

Gọi f(1) = A

\(3A=1.2.3+2.3.3+3.4.3+...+50.51.3\)

\(3A=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+50.51.\left(52-49\right)\)

\(3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+50.51.52-49.50.51\)

\(3A=50.51.52\)=44200

Vậy f(1) = 44200

Answer 2

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