đặt biểu thức trên =A
ta có: A=2/13.19+2/19.25+2/25.31+...+2/613.619
=(2/13-2/19)+(2/19-2/25)+(2/25-2/31)+...+(2/613-2/619)
=2/13-2/19+2/19-2/25+2/25-2/31+...+2/613-2/619
=2/13+(2/19-2/19)+(2/25-2/25)+(2/31-2/31)+...+(2/613-2/613)-2/619
=2/13-2/619=1212/8047
= 2 .[ \(\dfrac{1}{13.19}+\dfrac{1}{19.25}+\dfrac{1}{25.31}+........+\dfrac{1}{613.619}\)]
= 2 .[\(\dfrac{1}{6}\).(\(\dfrac{1}{13}-\dfrac{1}{19}\))+\(\dfrac{1}{6}\). (\(\dfrac{1}{19}-\dfrac{1}{25}\))+\(\dfrac{1}{6}\). (\(\dfrac{1}{25}-\dfrac{1}{31}\)) + ......+\(\dfrac{1}{6}\). (\(\dfrac{1}{613}-\dfrac{1}{619}\) ) ]
= 2. [\(\dfrac{1}{6}\).( \(\dfrac{1}{13}-\dfrac{1}{19}\)+\(\dfrac{1}{19}-\dfrac{1}{25}\)+\(\dfrac{1}{25}-\dfrac{1}{31}\)+ ......+\(\dfrac{1}{613}-\dfrac{1}{619}\))]
= 2. [\(\dfrac{1}{6}\).\(\dfrac{1}{619}\)]
=2 . \(\dfrac{1}{3714}\)
= \(\dfrac{1}{1857}\)
có j sai mọi người cứ nói
= 2 .[ 1/13.19+1/19.25+1/25.31+........+1/613.619]
= 2 .[1/6.(1/13−1/19 )+1/6. (1/19−1/25)+1/6. (1/25−1/31) + ......+1/6/. (1/613−1/619) ]
= 2. [1/6. 1/13− 1/6 .1/19/+1/6.1/19− 1/6.1/25/+ 1/6. 1/25− 1/6. 1/31+ ......+ 1/6. 1/613− 1/6. 1/619)]
= 2. [1/6.1/3- 1/6.1/619]
=2 . [1/6.(1/3 - 1/619]
= 2. [1/6 .616/1857]
= 2.308/5571
=616/5571
