thu gọn tổng sau D=4-4^2+4^3-4^4+………………+4^2019-4^2020

2 bình luận về “thu gọn tổng sau D=4-4^2+4^3-4^4+………………+4^2019-4^2020”

1. D = 4 – 4^2 + 4^3 – 4^4 + … + 4^(2019) – 4^(2020)

   D = ( 4 + 4^3 + … + 4^(2019) ) – ( 4^2 + 4^4 + … + 4^(2020) )

   Đặt A = 4 + 4^3 + … + 4^(2019)

   4^2A =  4^3 + 4^5 + … + 4^(2021)

   16A – A = ( 4^3 + 4^5 + … + 4^(2021) ) – ( 4 + 4^3 + … + 4^(2019) )

   15A = 4^(2021) – 4

   A = ( 4^(2021) – 4 )/15

   Đặt B = 4^2 + 4^4 + … + 4^(2020)

   4^2B = 4^4 + 4^6 + … + 4^(2022)

   16B – B = ( 4^4 + 4^6 + … + 4^(2022) ) – ( 4^2 + 4^4 + … + 4^(2020) )

   15B = 4^(2022) – 4^2

   B = ( 4^(2022) – 4^2 )/15

   => D = ( ( 4^(2021) – 4 )/15 ) – ( ( 4^(2022) – 4^2 )/15 )

   D = ( ( 4^(2021) – 4 ) – ( 4^(2022) – 4^2 ) )/15

   D = ( 4^(2021) – 4 – 4^(2022) + 16 )/15

   D = ( 4^(2021) – 4^(2022) + 12 )/15

   Trả lời
2. D=4-4^2+…+4^2019-4^2020

   => 4D=4^2-4^3+…+4^2020-4^2021

   => 4D+D=(4^2-4^3+…+4^2020-4^2021)+(4-4^2+…+4^2019-4^2020)

   => 5D=4-4^2021

   => D=(4-4^2021)/5

   Trả lời