a)A=1/1.3+1/3.5+1/5.7+…+1/19.21
b)B=1/99-1/99.98-1/98.97-1/97.96-1/3.2-1/2.1
a)A=1/1.3+1/3.5+1/5.7+…+1/19.21 b)B=1/99-1/99.98-1/98.97-1/97.96-1/3.2-1/2.1
By Parker
By Parker
a)A=1/1.3+1/3.5+1/5.7+…+1/19.21
b)B=1/99-1/99.98-1/98.97-1/97.96-1/3.2-1/2.1
a,
Ta có:
A= 1/1.3 + 1/3.5 + …..+ 1/5.7 +……+ 1/19.21
2.A = 2/1.3 + 2/3.5 + 2/5.7 +…+ 2/19.21
2.A= 1- 1/3+ 1/3- 1/5+ 1/5- 1/7+…………+ 1/19 – 1/21
2.A= 1- 1/21
2.A = 20/21
A= 20/21 : 2
A = 10/21
b,
B = 1/99 – 1/99.98 – 1/98.97 – ………….- 1/2.1
= 1/99 – ( 1/1.2 + 1/2.3 +…………..+ 1/98.99]
= 1/99 – ( 1- 1/2+ 1/2 – 1/3+ …………..+ 1/98 – 1/99]
= 1/99 – ( 1- 1/99]
= 1/99 – 98/88
= -97/99
~ Học tốt!~
Đáp án: A = $\frac{10}{21}$
B = $\frac{-97}{99}$
Giải thích các bước giải:
a ) A = $\frac{1}{1.3}$ + $\frac{1}{3.5}$ + $\frac{1}{5.7}$ + ….. + $\frac{1}{19.21}$
2A = $\frac{2}{1.3}$ + $\frac{2}{3.5}$ + $\frac{2}{5.7}$ + ….. + $\frac{2}{19.21}$
2A = 1 – $\frac{1}{3}$ + $\frac{1}{3}$ – $\frac{1}{5}$ + $\frac{1}{5}$ – $\frac{1}{7}$ + ….. + $\frac{1}{19}$ – $\frac{1}{21}$
2A = 1 – $\frac{1}{21}$
2A = $\frac{20}{21}$
A = $\frac{20}{21}$ : 2
A = $\frac{10}{21}$
b ) B = $\frac{1}{99}$ – $\frac{1}{99.98}$ – $\frac{1}{98.97}$ – $\frac{1}{97.96}$ – ….. – $\frac{1}{3.2}$ – $\frac{1}{2.1}$
B = $\frac{1}{99}$ – ( $\frac{1}{99.98}$ + $\frac{1}{98.97}$ + $\frac{1}{97.96}$ + ….. + $\frac{1}{3.2}$ + $\frac{1}{2.1}$ )
B = $\frac{1}{99}$ – ( $\frac{1}{1.2}$ + $\frac{1}{2.3}$ + ….. + $\frac{1}{96.97}$ + $\frac{1}{97.98}$ + $\frac{1}{98.99}$ )
B = $\frac{1}{99}$ – ( 1 – $\frac{1}{2}$ + $\frac{1}{2}$ – $\frac{1}{3}$ + ….. + $\frac{1}{96}$ – $\frac{1}{97}$ + $\frac{1}{97}$ – $\frac{1}{98}$ + $\frac{1}{98}$ – $\frac{1}{99}$ )
B = $\frac{1}{99}$ – ( 1 – $\frac{1}{99}$ )
B = $\frac{1}{99}$ – $\frac{98}{99}$
B = $\frac{-97}{99}$