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Câu hỏi

C h o h a ˋ m s o ^ ˊ f ′ ( x ) = ( 2 x + 1 ) ⋅ f 2 ( x ) v a ˋ f ( 1 ) = − 0 , 5. T ổ n g f ( 1 ) + f ( 2 ) + f ( 3 ) + … + f ( 2017 ) + f ( 2018 ) + f ( 2019 ) + f ( 2020 ) = b a ​ ; ( a ∈ ◻ ; b ∈ ◻ ) v ớ i b a ​ t o ^ ˊ i g i ả n . K h ẳ n g đ ị nh n a ˋ o s a u đ a ^ y đ u ˊ n g ?

R. Roboctvx76

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Giải thích

T a blank c ó colon blank f to the power of apostrophe left parenthesis x right parenthesis equals left parenthesis 2 x plus 1 right parenthesis times f squared left parenthesis x right parenthesis left right double arrow fraction numerator f to the power of apostrophe left parenthesis x right parenthesis over denominator f squared left parenthesis x right parenthesis end fraction equals 2 x plus 1 left right double arrow integral fraction numerator f to the power of apostrophe left parenthesis x right parenthesis over denominator f squared left parenthesis x right parenthesis end fraction d x equals integral left parenthesis 2 x plus 1 right parenthesis d x left right double arrow negative fraction numerator 1 over denominator f left parenthesis x right parenthesis end fraction equals x squared plus x plus C rightwards double arrow fraction numerator 1 over denominator f left parenthesis x right parenthesis end fraction equals negative x squared minus x minus C text .  end text L ạ i blank c ó colon blank f left parenthesis 1 right parenthesis equals negative 0 , 5 rightwards double arrow negative 2 equals negative 1 squared minus 1 minus C rightwards double arrow C equals 0. V ậ y blank fraction numerator 1 over denominator f left parenthesis x right parenthesis end fraction equals negative open parentheses x squared plus x close parentheses equals negative x left parenthesis x plus 1 right parenthesis blank h a y blank minus f left parenthesis x right parenthesis equals fraction numerator 1 over denominator x left parenthesis x plus 1 right parenthesis end fraction. T a blank c ó colon blank minus f left parenthesis 1 right parenthesis minus f left parenthesis 2 right parenthesis minus f left parenthesis 3 right parenthesis minus horizontal ellipsis minus f left parenthesis 2017 right parenthesis minus f left parenthesis 2018 right parenthesis minus f left parenthesis 2019 right parenthesis minus f left parenthesis 2020 right parenthesis equals fraction numerator 1 over denominator 1.2 end fraction plus fraction numerator 1 over denominator 2.3 end fraction plus fraction numerator 1 over denominator 3.4 end fraction plus fraction numerator 1 over denominator 2018.2019 end fraction plus fraction numerator 1 over denominator 2019.2020 end fraction plus fraction numerator 1 over denominator 2020 minus 2021 end fraction equals 1 minus 1 half plus 1 half minus 1 third plus 1 third minus 1 fourth plus horizontal ellipsis plus 1 over 2018 minus 1 over 2019 plus 1 over 2019 minus 1 over 2020 plus 1 over 2020 minus 1 over 2021 equals 1 minus 1 over 2021 equals 2020 over 2021 V ậ y blank f left parenthesis 1 right parenthesis plus f left parenthesis 2 right parenthesis plus f left parenthesis 3 right parenthesis plus horizontal ellipsis plus f left parenthesis 2020 right parenthesis equals fraction numerator negative 2020 over denominator 2021 end fraction blank h a y blank a equals negative 2020 comma b equals 2021 rightwards double arrow b minus a equals 4042.

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Câu hỏi tương tự

Giả sử ∫ x ( x + 1 ) ( x + 2 ) ( x + 3 ) + 1 ( 2 x + 5 ) a x ​ = − g ( x ) 1 ​ + C , (C là hằng số).Tính tổng các nghiệmthực của phương trình g ( x ) = 0

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