​cho P=1/2+1/3+1/4+...........+1/48+1/49+1/50 và Q=1/49+2/48+3/47+........+47/3+48/2+49/1

So sánh tổng : S = 1/5 + 1/9 + 1/10 + 1/41 + 1/42 với 1/2

S=

=50/50+50/49+50/48+...+50/2

=50.(1/50+1/49+1/48+...+1/4+1/3+1/2)

=50

P=

P=(1/49+1)+(2/48+1)+...+(48/2+1)+1

P= 50/49+50/48+....+50/2+50/50=1

vậy s/p = 1/50

P = 1/49+2/48+3/47+...+48/2+49/1

Cộng 1 váo mỗi p/s trong 48 p/s đầu , trừ p/s cuối đi 48 ta đượ

P=(1/49+1)+(2/48+1)+...+(48/2+1)+1

P= 50/49+50/48+....+50/2+50/50

Đưa ps cuối lên đầu

P=50/50+50/49+50/48+...+50/2

=50.(1/50+1/49+1/48+...+1/4+1/3+1/2)

=50.S

VậyS/P=1/50
 

1/50

 chúc bạn học tốt :-)))

SAI CHÍNH TẢ QUÁ NHIỀU

Q = \(\frac{1}{49}+\frac{2}{48}+\frac{3}{47}+...+\frac{48}{2}+\frac{49}{1}\)

Cộng 1 vào mỗi phân số trong 48 phân số đầu, trừ phân số cuối đi 48, ta được :

Q = \(\left(\frac{1}{49}+1\right)+\left(\frac{2}{48}+1\right)+\left(\frac{3}{47}+1\right)+...+\left(\frac{48}{2}+1\right)+1\)

Q = \(\frac{50}{49}+\frac{50}{48}+\frac{50}{47}+...+\frac{50}{2}+1\)

Q = \(\frac{50}{49}+\frac{50}{48}+\frac{50}{47}+...+\frac{50}{2}+\frac{50}{50}\)

đưa phân số cuối lên đầu :

Q = \(\frac{50}{50}+\frac{50}{49}+\frac{50}{48}+\frac{50}{47}+...+\frac{50}{2}\)

Q = \(50.\left(\frac{1}{50}+\frac{1}{49}+\frac{1}{48}+\frac{1}{47}+...+\frac{1}{2}\right)\)

Q = 50 . A

Vậy \(\frac{P}{Q}=\frac{1}{50}\)

\(S=\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{50}\)

\(\Rightarrow S=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}...+\dfrac{1}{49}-\dfrac{1}{50}\)

\(\Rightarrow S=1-\dfrac{1}{50}\)

\(\Rightarrow S=\dfrac{49}{50}\)

Phần P bạn xem lại đề

p=\(\frac{1}{49}+\frac{2}{48}+\frac{3}{47}+...+\frac{48}{2}+49\)

=\(\left(\frac{1}{49}+1\right)+\left(\frac{2}{48}+1\right)+\left(1+\frac{3}{47}\right)+...+\left(1+\frac{48}{2}\right)+\frac{50}{50}\)

=\(\frac{50}{50}+\frac{50}{49}+\frac{50}{48}+...+\frac{50}{2}\)

=\(50\left(\frac{1}{50}+\frac{1}{49}+\frac{1}{48}+...+\frac{1}{2}\right)\)

p=50*S

\(\frac{S}{\text{p}}=\frac{1}{50}\)

s=1,p=50