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Lý thuyết Cấp số nhân - SGK Toán 11 Cánh Diều

1. Định nghĩa

ℱTổng hợp đề thi học kì 2 lớp 11 tất cả các môn - Cánh diều

Toán - Văn - Anh - Lí - Hóa - Sinh
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1. Định nghĩa

Cấp số nhân là một dãy số, trong đó kể từ số hạng thứ hai, mỗi số hạng đều là tích của số hạng ngay trước nó với một số không đổi q. Tức là:\({u_n} = {u_{n - 1}}.q,n \in {\mathbb{N}^*}\)Số q được gọi là công bội của cấp số nhân.

* Chú ý:꧟ Dãy \(\left( {{u_n}} \right)\) là cấp số nhân thì \({u_k}^2 = {u_{k - 1}}.{u_{k + 1}}\left( {k \ge 2} \right)\).

2. Số hạng tổng quát

Nếu một cấp số nhân có số hạng đầu \({u_1}\) và công bội q thì số hạng tổng quát \({u_n}\)của nó được xác định bởi công thức\({u_n} = {u_1}.{q^{n - 1}},n \ge 2\)

3. Tổng của n số hạng đầu của một cấp số nhân

Cho cấp số nhân \(\left( {{u_n}} \right)\) với công bội \(q \ne 1\). Đặt \({S_n} = {u_1} + {u_2} + {u_3} + ... + {u_n}\). Khi đó\({S_n} = \frac{{{u_1}\left( {1 - {q^n}} \right)}}{{1 - q}}\)

 

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Tham Gia Group Dành Cho Lớp 11 Chia Sẻ, Trao Đổi Tài Liệu Miễn Phí

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