NT
5
K
Khách
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SL
9
8 tháng 4 2016
1/1.2+1/3.4+1/5.6+...+1/49.50=1/26+1/27+...+1/50
=1/1-1/2+1/3-1/4+...+1/49-1/50
=(1/1+1/3+...+1/49)-(1/2+1/4+...+1/50)
=(1/1+1/2+1/3+...+1/49+1/50)-2(1/2+1/4+...+1/50)
=1/1+1/2+1/3+...+1/50-1-1/2-1/3-...-1/25
=1/26+1/27+...+1/50 (đpcm)
ỦNg hộ nhà mih lại cho !!!
TT
1
AL
9 tháng 8 2016
\(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{49.50}\)
\(=\left(\frac{1}{1}-\frac{1}{2}\right)+...+\left(\frac{1}{49}-\frac{1}{50}\right)\)
\(=\frac{1}{1}-\frac{1}{50}\)
\(=\frac{49}{50}\)
P
2
TT
5 tháng 2 2020
Ta có : \(\frac{1}{1.2}+\frac{1}{3.4}+...+\frac{1}{49.50}\)
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\)
\(=\left(1+\frac{1}{2}+...+\frac{1}{50}\right)-2\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{50}\right)\)
\(=\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{50}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{25}\right)\)
\(=\frac{1}{26}+\frac{1}{27}+...+\frac{1}{50}\)
Khi đó : \(\left(\frac{1}{26}+\frac{1}{27}+...+\frac{1}{50}\right):\left(\frac{1}{1.2}+\frac{1}{3.4}+...+\frac{1}{49.50}\right)\)
\(=\left(\frac{1}{26}+\frac{1}{27}+...+\frac{1}{50}\right):\left(\frac{1}{26}+\frac{1}{27}+...+\frac{1}{50}\right)=1\) (đpcm)
XO
5 tháng 2 2020
Ta có : \(\frac{1}{1.2}+\frac{1}{3.4}+...+\frac{1}{49.50}=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\)
= \(\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{50}\right)-2\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{50}\right)\)
= \(\left(1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{50}\right)-\left(1+\frac{1}{2}+...+\frac{1}{25}\right)=\frac{1}{26}+\frac{1}{27}+...+\frac{1}{50}\)
Khi đó \(\frac{\frac{1}{26}+\frac{1}{27}+...+\frac{1}{50}}{\frac{1}{1.2}+\frac{1}{3.4}+...+\frac{1}{49.50}}=\frac{\frac{1}{26}+\frac{1}{27}+...+\frac{1}{50}}{\frac{1}{26}+\frac{1}{27}+...+\frac{1}{50}}=1\left(\text{đpcm}\right)\)
PL
15 tháng 4 2016
A=1/1.2+1/3.4+.....+1/49.50
=1-1/2+1/3-1/4+...+1/49-1/50=(1+1/3+1/5+...+1/49) - (1/2+1/4+1/6+...+1/50)
=(1+1/3+1/5+...+1/49)+(1/2+1/4+1/6+...+1/50)-2.(1/2+1/4+1/6+...+1/50)
=(1+1/2+1/3+1/4+...+1/49+1/50) - (1+1/2+1/3+...1/25)
=1/26+1/27+...1/50
Vậy .........
NT
1
30 tháng 4 2015
Ta có : \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-...-\frac{1}{50}\)
\(=1-\frac{1}{50}=\frac{49}{50}\)
Vì \(\frac{49}{50}<1\)
Nên \(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{49.50}<1\)
TL
2
8 tháng 4 2017
\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{49.50}< 1\)
Ta có: \(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{49.50}< 1\)
=\(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{49}-\dfrac{1}{50}< 1\)
= \(\dfrac{1}{1}-\dfrac{1}{50}< 1\)
= \(\dfrac{50}{50}+\dfrac{-1}{50}< 1\)
= \(\dfrac{49}{50}< 1\)
Vậy \(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{49.50}< 1\)
1/1.2+1/3.4+1/5.6+...+1/49.50=1/26+1/27+...+1/50
=1/1-1/2+1/3-1/4+...+1/49-1/50
=(1/1+1/3+...+1/49)-(1/2+1/4+...+1/50)
=(1/1+1/2+1/3+...+1/49+1/50)-2(1/2+1/4+...+1/50)
=1/1+1/2+1/3+...+1/50-1-1/2-1/3-...-1/25
=1/26+1/27+...+1/50 (đpcm)
1/1.2+1/3.4+1/5.6+...+1/49.50=1/26+1/27+...+1/50
=1/1-1/2+1/3-1/4+...+1/49-1/50
=(1/1+1/3+...+1/49)-(1/2+1/4+...+1/50)
=(1/1+1/2+1/3+...+1/49+1/50)-2(1/2+1/4+...+1/50)
=1/1+1/2+1/3+...+1/50-1-1/2-1/3-...-1/25
=1/26+1/27+...+1/50 (đpcm)
Hình như sai đề rồi bạn ạ
1/1.2+1/3.4+1/5.6+...+1/49.50=1/26+1/27+...+1/50
=1/1-1/2+1/3-1/4+...+1/49-1/50
=(1/1+1/3+...+1/49)-(1/2+1/4+...+1/50)
=(1/1+1/2+1/3+...+1/49+1/50)-2(1/2+1/4+...+1/50)
=1/1+1/2+1/3+...+1/50-1-1/2-1/3-...-1/25
=1/26+1/27+...+1/50
=> đpcm
Cre: http://olm.vn/hoi-dap/question/79077.html?auto=1
1/1.2 + 1/3.4 + 1/5.6 + ... + 1/49.50 = 1/26 + 1/27 + ... + 1/50
= 1/1 - 1/2 + 1/3 - 1/4 + ... + 1/49 - 1/50
= (1/1 + 1/3 + ... + 1/49) - (1/2 + 1/4 + ... + 1/50)
= (1/1 + 1/2 + 1/3 + ... + 1/49 + 1/50) - 2(1/2 + 1/4 + ... + 1/50)
= 1/1 + 1/2 + 1/3 + ... + 1/50 - 1 - 1/2 - 1/3 - ... - 1/25
= 1/26 + 1/27 + ... + 1/50
=> điều cần chứng minh