chung minh 1/3-2/3^2+3/3^3-4/3^4+...+99/3^99-100/3^100<3/16
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chung minh rang 1/3-2/3^2+3/3^3-4/3^4+....+99/3^99-100/3^100<3/16
chung minh rang 1/3 -1 /3^2 + 3/3^3 -4/3^4+...+99/3^99-100/3^100 < 3/16
cho n=1/3-2/3^2+3/3^3-4/3^4+...+99/3^99-100/3^100 . Chung minh n < 3/16
Chung minh rang: \(\frac{1}{3}-\frac{2}{3^2}+\frac{3}{3^3}-\frac{4}{3^4}+....+\frac{99}{3^{99}}-\frac{100}{3^{100}}<\frac{3}{16}\)
Dat A=1/3-2/32+3/33-4/34+...+99/399-100/3100
3A=1-2/3+3/32-4/33+...+99/398-100/399
3A+A=1-1/3+1/32-1/33+...+1/398-1/399-100/3100=4A
4A.3=3-1+1/3-1/32+...+1/397-1/398-100/399=12A
4A+12A=3-100/399-1/399-100/3100
16A=3-300/3100-3/3100-100/3100=3-403/3100<3
A<3/16
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Chung minh 1/1!+2/3!+3/4!+4/5!+...+99/100!<1
Chứng minh rằng 1/3-3/2^2+3/3^3-4/3^4+...+99/3^99-100/3^100
chung minh rang 1/2!+2/3!+3/4!+....+99/100!<1
chumg minh rang 1/3-2/3^2+3/3^3-4/3^4+...+99/3^99-100/3^100<3/16
chứng minh: 1/3-2/3^2+3/3^3-4/3^4+...+99/3^99-100/3^100<3/16