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\(2A=1+\frac{1}{2}+...+\frac{1}{2^{49}}\)
\(2A-A=1-\frac{1}{2^{50}}\)
\(A=1-\frac{1}{2^{50}}\)=> A bé hơn 1
tương tự nha
\(A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{49}}+\frac{1}{2^{50}}\)
\(2A=2.\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{49}}+\frac{1}{2^{50}}\right)\)
\(2A=1+\frac{1}{2}+\frac{1}{2^2}+....+\frac{1}{2^{48}}+\frac{1}{2^{49}}\)
\(2A-A=\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{48}}+\frac{1}{2^{49}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{49}}+\frac{1}{2^{50}}\right)\)
\(A=1-\frac{1}{2^{50}}< 1\)
B= (1/2-1/3) + (1/3-1/4) + (1/4-1/5)+...+( 1/99-1/100)
B = (1/2-1/3) + (1/3 - 1/4) + (1/4 - 1/5)+...+ (1/99 + 1/100)
B= 1/2 +1/100=51/100
k mk nhóe
sai thì chỉ mk nhoa
a)A=1/51+1/52+...+1/100
=>A>1/100+1/100+...+1/100
=>A>50/100(vì có 50 số hạng)
=> A>1/2
b)Ta có:
B=1/2.3+1/3.4+...+1/99.100
=> B=1/2-1/3+1/3-1/4+...+1/99-1/100
=> B=1/2-1/100
Mà 1/100>0
=> B<1/2
=> B<1/2<A
=>B<A
Với mọi \(x\in Z\) ta có:
\(1+2+3+..+n=\frac{n\left(n+1\right)}{2}\)
=> \(\frac{1}{1+2+3+..+n}=\frac{2}{n\left(n+1\right)}=2\left[\frac{1}{n\left(n+1\right)}\right]=2\left(\frac{1}{n}-\frac{1}{n+1}\right)\)
Có:
\(\frac{1}{1+2}=2\left(\frac{1}{2}-\frac{1}{3}\right)\)
\(\frac{1}{1+2+3}=2\left(\frac{1}{3}-\frac{1}{4}\right)\)
.......................................................
\(\frac{1}{1+2+3+4+...+99}=2\left(\frac{1}{99}-\frac{1}{100}\right)\)
Nên:
\(\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+...+\frac{1}{1+2+3+4+..+99}+\frac{1}{50}\)
\(=2\left(\frac{1}{2}-\frac{1}{3}\right)+2\left(\frac{1}{3}-\frac{1}{4}\right)+...+2\left(\frac{1}{99}-\frac{1}{100}\right)+\frac{1}{50}\)
\(=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\right)+\frac{1}{50}\)
\(=2\left(\frac{1}{2}-\frac{1}{100}\right)+\frac{1}{50}=2\cdot\frac{49}{100}+\frac{1}{50}=\frac{49}{50}+\frac{1}{50}=1\)
Cảm ơn bạn (chị ) nhiều !
Công nhận chị học giỏi thật đấy !
3. S= -1/6 + -1/20 + 1/10 + 1/6
=0
4. A= -1 -1 -1 -1 -.... -1 [ có (50-2): 2 +1 = 25 số -1)
=-25
2Q = 1-1/3-1/2+1/4+1/3-1/5-1/4+1/6-........+1/97-1/99-1/98+1/100 = 1-1/2-1/99+1/100 = 4949/9900 >> Q = 49499/19800
\(Q=\frac{1}{1.3}-\frac{1}{2.4}+\frac{1}{3.5}-\frac{1}{4.6}+...+\frac{1}{97.99}-\frac{1}{98.100}\)
\(=\frac{1}{2}\left(1-\frac{1}{3}-\frac{1}{2}+\frac{1}{4}+\frac{1}{3}+\frac{1}{5}-\frac{1}{4}+\frac{1}{6}+...+\frac{1}{97}-\frac{1}{99}-\frac{1}{98}+\frac{1}{100}\right)\)
\(=\frac{1}{2}\left(1-\frac{1}{100}\right)=\frac{1}{2}.\frac{99}{100}=\frac{99}{200}\) (không chắc cho lắm :v)
1/1+2+1/1+2+3+1/1+2+3+4+...+1/1+2+3+...+99 +1/50
=1/(2+1).2:2+1/(3+1).3:2+1/(4+1).4:2+..+1/(99+1).99:2+1/50
=2/2.3+2/3.4+2/4.5+..+2/99.100+1/50
=2(1/2.3+1/3.4+1/4.5+..+1/99.100)+1/50
=2(1/2-1/3+1/3-1/4+1/4-1/5+...+1/99-1/100)+1/50
=2(1/2-1/100)+1/50
=49/50+1/50=1