數學ques...

公比: -27/81
= -1/3

首項: 81

設級數的項數是n,
81 (-1/3)^(n-1) = -1/27
(-1/3)^(n-1) = -1/2187
(-1/3)^(n-1) = (-1/3)^7
所以, n = 8.

求各級數的和:
81 - 27 + 9 - ......... -1/27
= {(81)[1-(-1/3)^8]}/[1-(-1/3)] 用公式 : [a (1 - r^n)]/(1 - r)
= [(81)(1-1/6561)]/(4/3)
= [(81)(6560/6561)]/(4/3)
= (6560/81)/(4/3)
= (6560/81)*(3/4)
= 1640/27

有問題歡迎提出!

1640/27

求各級數的和

81 - 27 + 9 - ......... --1/27 (等比)
81=3^4
1/27=3^-3
所以項數=4-(-3)+1=8
首項=81
公比=-1/3
81 - 27 + 9 - ......... -1/27
=81[1-(-1/3)^8]/[1-(-1/3)]
=[81-(1/81)]/(4/3)
=3(81^2-1)/324
= 19680/324
=1640/27

1640/27