Toán Tinh (M-N) ² với M=1-1/2+1/3-1/4+…+1/2017-1/2018+1/2019 va N=1/1010+1/1011+…+1/2019 06/10/2021 By aihong Tinh (M-N) ² với M=1-1/2+1/3-1/4+…+1/2017-1/2018+1/2019 va N=1/1010+1/1011+…+1/2019
Đáp án + Giải thích các bước giải: Ta có : `M=1-1/2+1/3-1/4+…+1/2017-1/2018+1/2019` `=(1+1/3+….+1/2017+1/2019)-(1/2+1/4+…+1/2018)` `=(1+1/2+1/3+1/4+…+1/2017+1/2018+1/2019)-2-(1/2+1/4+…+1/2018)` `=1/1010+1/1011+….+1/2019` `=> (M-N)^2=[(1/1010+1/1011+….+1/2019)-(1/1010+1/1011+….+1/2019)]^2` `=0` Trả lời
Ta có: M= 1 -1/2 + 1/3 – 1/4 +….+ 1/2017 – 1/2018 + 1/2019 M= (1 + 1/3 +…..+ 1/2017 + 1/2019) – (1/2 + 1/4+….+ 1/2018) M = (1 + 1/3 + 1/2017 + 1/2019 +1 + 1/2 +…+ 1/1009) – 2(1/2 + 1/4+….+ 1/2018) M= 1 + 1/2 + 1/3 + 1/4+…+ 1/2018 + 1/2019 – 1 -1/2 -…..- 1/1009 M= 1/1010 + 1/1011 + ….+ 1/2019 => (M-N)² = ( 1/1010 + 1/1011 + ….+ 1/2019 – 1/1010 – 1/1011 -….-1/2019) => (M-N)² = 0² =0 Vậy (M-N)² =0 Trả lời
Đáp án + Giải thích các bước giải:
Ta có : `M=1-1/2+1/3-1/4+…+1/2017-1/2018+1/2019`
`=(1+1/3+….+1/2017+1/2019)-(1/2+1/4+…+1/2018)`
`=(1+1/2+1/3+1/4+…+1/2017+1/2018+1/2019)-2-(1/2+1/4+…+1/2018)`
`=1/1010+1/1011+….+1/2019`
`=> (M-N)^2=[(1/1010+1/1011+….+1/2019)-(1/1010+1/1011+….+1/2019)]^2`
`=0`
Ta có:
M= 1 -1/2 + 1/3 – 1/4 +….+ 1/2017 – 1/2018 + 1/2019
M= (1 + 1/3 +…..+ 1/2017 + 1/2019) – (1/2 + 1/4+….+ 1/2018)
M = (1 + 1/3 + 1/2017 + 1/2019 +1 + 1/2 +…+ 1/1009) – 2(1/2 + 1/4+….+ 1/2018)
M= 1 + 1/2 + 1/3 + 1/4+…+ 1/2018 + 1/2019 – 1 -1/2 -…..- 1/1009
M= 1/1010 + 1/1011 + ….+ 1/2019
=> (M-N)² = ( 1/1010 + 1/1011 + ….+ 1/2019 – 1/1010 – 1/1011 -….-1/2019)
=> (M-N)² = 0² =0
Vậy (M-N)² =0