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Câu 13 trang 225 SGK Đại số và Giải tích 11 Nâng cao

Cho dãy số (un) xác định bởi
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Cho dãy số (un) xác định bởi

\({u_1} = 5\,\text{ và }\,{u_n} = {u_{n - 1}} - 2\) với mọi n ≥ 2

LG a

Hãy tìm số hạng tổng quát của dãy số (un)

Lời giải chi tiết:

Ta có: \({u_{n + 1}} - {u_n} =  - 2;\forall n \ge 1\)

Suy ra: (un) là một cấp số cộng có số hạng đầu u1 = 5 và công sai d = -2 do đó :

\({u_n} = {u_1} + \left( {n - 1} \right)d \) \(= 5 + \left( {n - 1} \right)\left( { - 2} \right) =  - 2n + 7\)

LG b

Hãy tính tổng 100 số hạng đầu tiên của dãy số (un).

Lời giải chi tiết:

\({S_{100}} = {{100} \over 2}\left( {2{u_1} + 99d} \right) \) \(= 50\left( {10 - 198} \right) =  - 9400\)

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