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Câu 38 trang 121 SGK Đại số và Giải tích 11 Nâng cao

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Hãy chọn những khẳng định đúng trong các khẳng định dưới đây :

LG a

Nếu các số thực a, b, c mà \(abc ≠ 0\), theo thứ tự đó lập thành một cấp số cộng với công sai khác 0 thì các số \({1 \over a},{1 \over b},{1 \over c}\) theo thứ tự đó cũng lập thành một cấp số cộng.

Lời giải chi tiết:

Sai vì \(1, 2, 3\) là cấp số cộng nhưng \(1,{1 \over 2},{1 \over 3}\) không là cấp số cộng.

LG b

Nếu các số thực a, b, c mà \(abc ≠ 0\), theo thứ tự đó lập thành một cấp số nhân thì các số \({1 \over a},{1 \over b},{1 \over c}\) theo thứ tự đó cũng lập thành một cấp số nhân.

Lời giải chi tiết:

Đúng vì nếu \(a, b, c\) là cấp số nhân công bội \(q ≠ 0\) thì \({1 \over a},{1 \over b},{1 \over c}\) là cấp số nhân công bội  \({1 \over q}.\)

LG c

\(1 + \pi + {\pi ^2} + ... + {\pi ^{100}} = {{{\pi ^{100}} - 1} \over {\pi - 1}}\)

Phương pháp giải:

Sử dụng công thức tổng CSN: \[{S_n} = \frac{{{u_1}\left( {1 - {q^n}} \right)}}{{1 - q}}\]

Lời giải chi tiết:

Sai vì dãy \(1,\pi ,{\pi ^2},...{\pi ^{100}}\) là một CSN có 101 số hạng và \({u_1} = 1,q = \pi \). Tổng 101 số hạng trên là: \(S_{101}=1 + \pi + {\pi ^2} + ... + {\pi ^{100}} \) \( = \frac{{1.\left( {1 - {\pi ^{101}}} \right)}}{{1 - \pi }}\) \(= {{{\pi ^{101}} - 1} \over {\pi - 1}}\)

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