bài cuối bài thi giữa kì ii chứng minh 1/3-2/3^2+3/3^3-3/3^4+……+99/3^99-100/3^100< 3/16 14/09/2021 Bởi Margaret bài cuối bài thi giữa kì ii chứng minh 1/3-2/3^2+3/3^3-3/3^4+……+99/3^99-100/3^100< 3/16
Đáp án: Giải thích các bước giải: →3A=1-2/3+3/3^2-4/3^3+…+99/3^98-100/3^99 4A=3A+A=(1-2/3+3/3^2-4/3^3+…+99/3^98-100/3^99)+(1/3-2/3^2+…+99/3^99-100/3^100) 4A=1-1/3+1/3^2-1/3^3+…+1/3^98-1/3^99-100/3^100 12A=3-1+…+1/3^97-1/3^98-100/3^99 16A=4A+12A=(1-1/3+1/3^2-1/3^3+…+1/3^98-1/3^99-100/3^100)+(3-1+…+1/3^97-1/3^98-100/3^99) 16A=3-101/3^99-100/3^100<3 16A<3 A<3:16=3/16 Vậy A<3/16 Đánh máy khá lâu. Xin lỗi! Bình luận
Đáp án: Đặt A=1/3-2/3^2+3/3^3-3/3^4+……+99/3^99-100/3^100 =3A=1-2/3+3/3^2-4/3^3+…+99/3^98-100/3^99 =4A=3A+A=(1-2/3+3/3^2-4/3^3+…+99/3^98-100/3^99)+(1/3-2/3^2+…+99/3^99-100/3^100) =4A=1-1/3+1/3^2-1/3^3+…+1/3^98-1/3^99-100/3^100 =12A=3-1+…+1/3^97-1/3^98-100/3^99 =16A=4A+12A=(1-1/3+1/3^2-1/3^3+…+1/3^98-1/3^99-100/3^100)+(3-1+…+1/3^97-1/3^98-100/3^99) =16A=3-101/3^99-100/3^100<3 =>16A<3 =>A<`3/16` Đề này mình thi vào cuối kì 2 lớp 6 cả trường ko ai làm được Bình luận
Đáp án:
Giải thích các bước giải:
→3A=1-2/3+3/3^2-4/3^3+…+99/3^98-100/3^99
4A=3A+A=(1-2/3+3/3^2-4/3^3+…+99/3^98-100/3^99)+(1/3-2/3^2+…+99/3^99-100/3^100)
4A=1-1/3+1/3^2-1/3^3+…+1/3^98-1/3^99-100/3^100
12A=3-1+…+1/3^97-1/3^98-100/3^99
16A=4A+12A=(1-1/3+1/3^2-1/3^3+…+1/3^98-1/3^99-100/3^100)+(3-1+…+1/3^97-1/3^98-100/3^99)
16A=3-101/3^99-100/3^100<3
16A<3
A<3:16=3/16
Vậy A<3/16
Đánh máy khá lâu. Xin lỗi!
Đáp án:
Đặt A=1/3-2/3^2+3/3^3-3/3^4+……+99/3^99-100/3^100
=3A=1-2/3+3/3^2-4/3^3+…+99/3^98-100/3^99
=4A=3A+A=(1-2/3+3/3^2-4/3^3+…+99/3^98-100/3^99)+(1/3-2/3^2+…+99/3^99-100/3^100)
=4A=1-1/3+1/3^2-1/3^3+…+1/3^98-1/3^99-100/3^100
=12A=3-1+…+1/3^97-1/3^98-100/3^99
=16A=4A+12A=(1-1/3+1/3^2-1/3^3+…+1/3^98-1/3^99-100/3^100)+(3-1+…+1/3^97-1/3^98-100/3^99)
=16A=3-101/3^99-100/3^100<3
=>16A<3
=>A<`3/16`
Đề này mình thi vào cuối kì 2 lớp 6
cả trường ko ai làm được