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Toán Lớp 6: A= 1/5^1 − 1/5^3 + 1/5^5 − 1/5^7+… + 1/5^99 − 1/5^101 < 1 5 B = 151+ 1/52+ 1/53+ 1/54+ ⋯ . + 1/150< 3

Home/ Toán Lớp 6: A= 1/5^1 − 1/5^3 + 1/5^5 − 1/5^7+… + 1/5^99 − 1/5^101 < 1 5 B = 151+ 1/52+ 1/53+ 1/54+ ⋯ . + 1/150< 3

Toán Lớp 6: A= 1/5^1 − 1/5^3 + 1/5^5 − 1/5^7+… + 1/5^99 − 1/5^101 < 1 5 B = 151+ 1/52+ 1/53+ 1/54+ ⋯ . + 1/150< 3

Hoàng Hà Tháng Mười Hai 26, 2022 Toán học 1 Comment 0 views

Toán Lớp 6: A= 1/5^1 − 1/5^3 + 1/5^5 − 1/5^7+… + 1/5^99 − 1/5^101 < 1 5 B = 151+ 1/52+ 1/53+ 1/54+ ⋯ . + 1/150< 3

Comments ( 1 )

huyenmi76
26 Tháng Mười Hai, 2022 at 12:28 chiều

Reply

A= 1/5^1- 1/5^3 + 1/5^5 – 1/5^7+… + 1/5^99 – 1/5^101

= 1/5 – (1/5^3 – 1/5^5) – (1/5^7 – 1/5^9)-… – (1/5^97 – 1/5^99) – 1/5^101

Ta có:

1/5^3 > 1/5^5 => 1/5^3 – 1/5^5 > 0

1/5^7 > 1/5^9 => 1/5^7 – 1/5^9 > 0

………………….

1/5^97 > 1/5^99 => 1/5^97 – 1/5^99 > 0

mà 1/5^101 > 0

=> 1/5 – (1/5^3 – 1/5^5) – (1/5^7 – 1/5^9)-… – (1/5^97 – 1/5^99) – 1/5^101 < 1/5

=> A < 1/5 (đpcm)

————————————————

B = 1/51+ 1/52+ 1/53+ 1/54+ ….. + 1/150 (100 số hạng)

< 1/51+ 1/51+ 1/51+ 1/51+ ….. + 1/51 (100 số hạng)

= 100/51 < 2

mà 2 < 3

=> 1/51+ 1/52+ 1/53+ 1/54+ ….. + 1/150 < 3

=> B < 3 (đpcm)

(Chúc bạn học tốt)

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