解答

✨ 最佳解答 ✨


等比級數公式:
Sn = a1(1 - r^n) / (1 - r)

Sn
= 1[1 - (1/3)^n] / (1 - 1/3)
= 3/2 - (3/2)(1/3)^n

3/2 - Sn = (3/2)(1/3)^n < 3*10^(-4)
=> 3^(-n) < 2*10^(-4)
以下的也能用試選項試出來 不用這樣寫
=> 10^(-nlog3) < 10^(log2 - 4)
=> -nlog3 < log2 - 4
=> -0.4771n < -3.6990
=> n > 7.75
=> n = 8


等比數列頭尾兩項相乘 = 中項^2
前9項乘積
= (a1*a9)(a2*a8)(a3*a7)(a4*a6)(a5)
= a5^9
= 125^3
a5 = 5
a4*a6 = 25


Sn = 2*n^2 - 5
a1 = S1 = -3
a2 = S2 - S1 = 6
an
= Sn - S(n-1)
= (2*n^2 - 5) - [2*(n-1)^2 - 5]
= 4n - 2
=> 等差數列的一般式
a100 = 400 - 2 = 398

Leeyee

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