ta co:

2A=2(2 mu 60 +1 /2 mu 61 +1)

2A=2 mu 61 +2 / 2 mu 61 +1

2A=2 mu 61 +1+1/2 mu 61 +1

2A=1+1/2 mu 61 +1

ta co:

2B=2(2 mu 61 +1/2 mu 62 +1)

2B=2 mu 62 +2/2 mu 62+1

2B=2 mu 62 +1+1/2 mu 62 +1

2B=1+1/2 mu 62 +1

mà 1+1/2 mu 61+1>1+1/2 mu 62 +1 nen 2A >2B

vậy A>B

nhớ k đúng cho mk nha

Ta có:

2.A=2 mủ 61 +2/2 mủ 61 +1=1+(2/2 mủ 61 +1)

2.B=2 mủ 62 + 2 /2 mủ 62 +1=1+(2/2 mủ 62 + 1)

vì ... nên 2.A >2.B.Vậy A>B

\(A=\frac{5^{60}+1}{5^{61}+1}\)

\(5A=\frac{5(5^{60}+1)}{5^{61}+1}=\frac{5^{61}+5}{5^{61}+1}=\frac{5^{61}+1+4}{5^{61}+1}=1+\frac{4}{5^{61}+1}\)                            \((1)\)

\(B=\frac{5^{61}+1}{5^{62}+1}\)

\(5B=\frac{5(5^{61})+1}{5^{62}+1}=\frac{5^{62}+5}{5^{62}+1}=\frac{5^{62}+1+4}{5^{62}+1}=1+\frac{4}{5^{62}+1}\)                          \((2)\)

Từ 1 và 2 \(\Rightarrow1+\frac{4}{5^{61}+1}>1+\frac{4}{5^{62}+1}\)

\(\Rightarrow5A>5B\)

Hay \(A>B\)

Vậy : ...

\(A=\frac{1}{5}+\left(\frac{1}{13}+\frac{1}{14}+\frac{1}{15}\right)+\left(\frac{1}{61}+\frac{1}{62}+\frac{1}{63}\right)

Ta có :

\(\frac{1}{13}< \frac{1}{12};\frac{1}{14}< \frac{1}{12};\frac{1}{15}< \frac{1}{12}\Rightarrow\frac{1}{13}+\frac{1}{14}+\frac{1}{15}< \frac{1}{12}+\frac{1}{12}+\frac{1}{12}=\frac{1}{4}\)

\(\frac{1}{61}< \frac{1}{60};\frac{1}{62}< \frac{1}{60};\frac{1}{63}< \frac{1}{60}\Rightarrow\frac{1}{61}+\frac{1}{62}+\frac{1}{63}< \frac{1}{60}+\frac{1}{60}+\frac{1}{60}=\frac{1}{20}\)

\(\Rightarrow D=\frac{1}{5}+\left(\frac{1}{13}+\frac{1}{14}+\frac{1}{15}\right)+\left(\frac{1}{61}+\frac{1}{62}+\frac{1}{63}\right)< \frac{1}{5}+\frac{1}{4}+\frac{1}{20}=\frac{1}{2}\)

Vậy \(D< \frac{1}{2}\)

\(D=\frac{1}{5}+\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{61}+\frac{1}{62}+\frac{1}{63}=\frac{1}{5}+\left(\frac{1}{13}+\frac{1}{14}+\frac{1}{15}\right)+\left(\frac{1}{61}+\frac{1}{62}+\frac{1}{63}\right)\)

Nhận xét: \(\frac{1}{13}+\frac{1}{14}+\frac{1}{15}< \frac{1}{12}+\frac{1}{12}+\frac{1}{12}=\frac{3}{12}=\frac{1}{4}\)

\(\frac{1}{61}+\frac{1}{62}+\frac{1}{63}< \frac{1}{60}+\frac{1}{60}+\frac{1}{60}=\frac{3}{60}=\frac{1}{20}\)

\(\Rightarrow D< \frac{1}{5}+\frac{1}{4}+\frac{1}{20}=\frac{1}{2}\)

Vậy D < 1/2

S=1/5+(1/13+1/14+1/15)+(1/61+1/62+1/63)

suy ra S<1/5+1/12.3+1/60.3

S<1/5+1/4+1/20

S<1/2 

S<1/2