Toán Lớp 7: 132 + 1/3 mũ 2 + 1/3 mũ 3 + chấm chấm chấm + 1/2 mũ 2020 giúp mik vs mn

Question

Toán Lớp 7:  132 + 1/3 mũ 2 + 1/3 mũ 3 + chấm chấm chấm + 1/2 mũ 2020 giúp mik vs mn

mocmien87 · Answer

Giải đáp:   $  $   Đề  1/3 + 1/3^2 + 1/3^3 + ... + 1/3^{2020}   Đặt A = 1/3 + 1/3^2 + 1/3^3 + ... + 1/3^{2020}   &harr; 3A = 3 (1/3 + 1/3^2 + 1/3^3 + ... + 1/3^{2020})   &harr; 3A = 1 + 1/3 + 1/3^2 + ... + 1/3^{2019}   &harr; 3A - A = (1 + 1/3 + 1/3^2 + ... + 1/3^{2019})- (1/3 + 1/3^2 + 1/3^3 + ... + 1/3^{2020})   &harr; (3-1) A= 1 - 1/3^{2020}   &harr; 2A =1 - 1/3^{2020}   &harr; A = (1 - 1/3^{2020})/2   Vậy A = (1 - 1/3^{2020})/2   $  $   Đề 1/2 + 1/2^2 + 1/2^3 + ... + 1/2^{2020}   Đặt A = 1/2 + 1/2^2 + 1/2^3 + ... + 1/2^{2020}   &harr; 2A = 2 (1/2 + 1/2^2 + 1/2^3 + ... + 1/2^{2020})   &harr; 2A = 1 + 1/2 + 1/2^2 + ... + 1/2^{2019}   &harr; 2A - A = (1 + 1/2 + 1/2^2 + ... + 1/2^{2019}) - (1/2 + 1/2^2 + 1/2^3 + ... + 1/2^{2020})   &harr; (2-1)A = 1 - 1/2^{2020}   &harr; A = 1 - 1/2^{2020}   Vậy A = 1- 1/2^{2020}

maitrucloan · Answer

Đặt A=1/3+1/3^2+1/3^3+...+1/3^2020   &rArr;3A=1+1/3+1/3^2+...+1/3^2019   &rArr;3A-A=(1+1/3+1/3^2+...+1/2^2019)-(1/3+1/3^2+1/3^3+...+1/3^2020)   &rArr;2A=1-1/3^2020   &rArr;2A={3^2020-1}/3^2020   &rArr;A={3^2020-1}/3^2021