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Toán Lớp 6: Cho P=2-2^2+2^3-2^4+…+2^99-2^100.Rút gọn P

Home/ Toán Lớp 6: Cho P=2-2^2+2^3-2^4+…+2^99-2^100.Rút gọn P

Toán Lớp 6: Cho P=2-2^2+2^3-2^4+…+2^99-2^100.Rút gọn P

Diễm Phúc Tháng Sáu 24, 2022 Toán học 2 Comments 0 views

Toán Lớp 6: Cho P=2-2^2+2^3-2^4+…+2^99-2^100.Rút gọn P

Comments ( 2 )

quynhthanhnghi
24 Tháng Sáu, 2022 at 7:02 sáng

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Giải đáp : P = \frac{2 – 2^101}{3}

P = 2 – 2^2 + 2^3 – 2^4 + … + 2^99 – 2^100

⇒ 2P = 2^2 – 2^3 + 2^4 – 2^5 + … + 2^100 – 2^101

⇒ 2P + P = (2^2 – 2^3 + 2^4 – 2^5 + … + 2^100 – 2^101) + (2 – 2^2 + 2^3 – 2^4 + … +2^99 – 2^100)

⇒ 3P = (2^2 – 2^2) + (2^3 – 2^3) + …. + (2^100 – 2^100) + 2 – 2^101

⇒ 3P = 2 – 2^101

⇒ P = \frac{2 – 2^101}{3}
kimoanh34
24 Tháng Sáu, 2022 at 7:02 sáng

Reply

P = 2 – 2^2 + 2^3 – 2^4 +……………………+ 2^99 – 2^100

2P = 2^2 – 2^3 + 2^4 – 2^5 + ………………………. + 2^100 – 2^101

2P + P = (2^2 – 2^3 + 2^4 – 2^5 +…………………… + 2^100 – 2^101) + (2 – 2^2 + 2^3 – 2^4 +………………. +2^99 – 2^100)

3P = (2^2 – 2^2) + (2^3 – 2^3) +…………………………+ (2^100 – 2^100) + 2 – 2^101

3P=2-2^101

P=(2-2^101)/3

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