Cmr
1/3-2/3^2+3/3^3-4/4^4+...+99/3^99-100/3^100<3/16
Giúp mk với mấy bn
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Cmr1/3-2/3^2+3/3^3-4/3^4+........+99/3-100/3^100<3/16
S=1×2+2×3+3×4+4×5+...........+99×100
3S=1×2×3+2×3×(4-1)+3×4×(5-2)+4×5×(6-3)+............+99×100×(101-98)
3S=1×2×3+2×3×4-1×2×3+3×4×5-2×3×4+4×5×6-3×4×5+.............+99×100×101-98×99×100
3S=99×100×101
Tại sao 3S=99×100×101
Các bạn giải thích hộ mình với!
MÌNH CẢM ƠN MỌI NGƯỜI!
S=1×2+2×3+3×4+4×5+...........+99×100
3S=1×2×3+2×3×(4-1)+3×4×(5-2)+4×5×(6-3)+............+99×100×(101-98)
3S=1×2×3+2×3×4-1×2×3+3×4×5-2×3×4+4×5×6-3×4×5+.............+99×100×101-98×99×100
3S=99×100×101
Tại sao 3S=99×100×101
Các bạn giải thích hộ mình với!
MÌNH CẢM ƠN MỌI NGƯỜI!
bài 1
A=1*2*3+2*3*4+3*4*5+...+99*100*101
B=1*3*5+3*5*7+...+95*97*99
C=2*4+4*6+..+98*100
D=1*2+3*4+5*6+...+99*100
E=1^2+2^2+3^2+...+100^2
G=1*3+2*4+3*5+4*6+...+99*101+100*102
H=1*2^2+2*3^2+3*4^2+...+99*100^2
I=1*2*3+3*4*5+5*6*7+7*8*9+...+98*99*100
K=1^2+3^2+5^2+...+99^2
A = 1*2*3 + 2*3*4 + 3*4*5 ... + 99*100*101
=> 4A = 1*2*3*4 + 2*3*4*4 + 3*4*5*4 + ... +99*100*101*4
=> 4A = 1*2*3*4 + 2*3*4*(5 - 1) + 3*4*5*( 6 - 2) + ... + 99*100*101*(102 - 98)
=> 4A = 1*2*3*4 + 2*3*4*5 - 1*2*3*4 + 3*4*5*6 - 2*3*4*5 + ... + 99*100*101*102 - 98*99*100*101
=> 4A = 99*100*101*102
=> 4A = 101989800
=> A = 25497450
tính nhanh (2/3+3/4+5/6+...+99/100).(1/2+2/3+3/4+...+98/99)-(1/2+1/3+...+99/100).(2/3+2/4+...+98/99)
tính 1/3 - 2/3^2 + 3/3^3 - 4/3^4..... + 99/3^99 - 100/3^100
1/3 - 2/3^2 + 3/3^2 - 4/3^4+ ... + 99/3^99 - 100 / 3^100 < 3/16
1/3 - 2/3^2 +3/3^3 - 4/3^4 +.......+99/3^99 - 100/3^100<3/16=?
1/3-2/3^2+3/3^3-4/3^4+...+99/3^99-100/3^100<3/16
k cho tôi đấy nhá An
Đặt A=\(\frac{1}{3}-\frac{2}{3^2}+\frac{3}{3^3}-\frac{4}{3^4}+..+\frac{99}{3^{99}}-\frac{100}{3^{100}}\)
=>3A=\(1-\frac{2}{3}+\frac{3}{3^2}-\frac{4}{3^3}+..+\frac{99}{3^{98}}-\frac{100}{3^{99}}\)
+A=\(\frac{1}{3}-\frac{2}{3^2}+\frac{3}{3^3}-\frac{4}{3^4}+..+\frac{99}{3^{99}}-\frac{100}{3^{100}}\)
=>4A= 1 - 1/3 + 1/3^2 - 1/3^3 +...+ 1/3^98 - 1/3^99 - 100/3^100
=>4A<1 - 1/3 + 1/3^2 - 1/3^3 +...+ 1/3^98 -1/3^99
=>4A<1-(1/3 -1/3^2+1/3^3-...-1/3^98+1/3^99)
Đặt B=1/3 -1/3^2+1/3^3-...-1/3^98+1/3^99
=>3B=1 - 1/3 +1/3^2 -... - 1/3^97 +1/3^98
=>4B=1+1/3^99>1
=>4B>1
=>B>1/4
=>-B<-1/4
=>1-B<1-1/4
=>4A<1-B<3/4
=>4A<3/4
=>A<3/4 : 4=3/16
=>A<3/16 (đpcm)
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1/3-2/3^2+3/3^3-4/3^4+..........+99/3^99-100/3^100<3/16