Bài $7$ . Thu gọn tổng sau: $A$ $=$ $1 + 3 +$ $3^{2} +$ $3^{3} +$ $\dots . . +$ $3^{100}$

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Bài $7$ . Thu gọn tổng sau: $A$ $=$ $1 + 3 +$ $3^{2} +$ $3^{3} +$ $\dots . . +$ $3^{100}$

Question

Bài $7$ . Thu gọn tổng sau:
$A$ $=$ $1 + 3 +$ $3^{2} +$ $3^{3} +$ $\dots . . +$ $3^{100}$

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Môn Toán Eirian 4 years 2020-11-11T15:22:04+00:00 2020-11-11T15:22:04+00:00 2 Answers 78 views 0

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Captcha* Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )

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Bo · Answer 1 · 2020-11-11T15:23:43+00:00

Bo

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2020-11-11T15:23:43+00:00 November 11, 2020 at 3:23 pm

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Ta có: `A = 1 + 3 + 3^2 + … + 3^100`

`3A = 3 + 3^2 + 3^3 + … + 3^101`

`→ 3A – A = 3^101 – 1`

`→ 2A = 3^101 – 1`

`→ A = (3^101 – 1)/2`

Jezebel · Answer 2 · 2020-11-11T15:23:59+00:00

Jezebel

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2020-11-11T15:23:59+00:00 November 11, 2020 at 3:23 pm

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$A = 1 + 3 + 3^{2} + 3^{3} + \dots . . + 3^{100}$

$3 A = 3 + 3^{2} + 3^{3} + 3^{4} + \dots . . + 3^{101}$

Ta lấy :

$3 A - A = (3 + 3^{2} + 3^{3} + 3^{4} + \dots . . + 3^{101}) - (1 + 3 + 3^{2} + 3^{3} + \dots . . + 3^{100})$

$2 A = 3^{101}$ -1

A = A = $\frac{3^{101} - 1}{2}$

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