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Bài 2.18 trang 56 SGK Toán 11 tập 1 - Cùng khám phá

Tìm tổng các số nguyên dương có ba chữ số và chia hết cho 3.
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Đề bài

Tìm tổng các số nguyên dương có ba chữ số và chia hết cho 3.

Phương pháp giải - Xem chi tiết

Từ đầu bài, xác định \({u_1},d,{u_n},n\). Áp dụng công thức để tính tổng: \(S = \frac{{n\left( {{u_1} + {u_n}} \right)}}{2}\)

Lời giải chi tiết

Các số nguyên dương có ba chữ số và chia hết cho 3 cách đều nhau 3 đơn vị nên ta lập được cấp số cộng với \({u_1} = 102,d = 3\).Số hạng cuối cùng của dãy là 999. Suy ra số số hạng của dãy là \(\frac{{999 - 102}}{3} + 1 = 300\).Vậy tổng các số nguyên dương có 3 chữ số và chia hết cho 3 là \(S = \frac{{n\left( {{u_1} + {u_n}} \right)}}{2} = \frac{{300\left( {102 + 999} \right)}}{2} = 165150\).

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