1/99 -1/99 x 97 - 1/97 x 95 - ... - 1/3 x 1
Giải pt : ( x-1/99 +x-99 )+( x-3/97 + x-97/3 )+ (x-5/95 + x-95/5 )=6
\(\Leftrightarrow\left(\dfrac{x-1}{99}-1\right)+\left(\dfrac{x-99}{1}-1\right)+\left(\dfrac{x-3}{97}-1\right)+\left(\dfrac{x-97}{3}-1\right)+\left(\dfrac{x-5}{95}-1\right)+\left(\dfrac{x-95}{5}-1\right)=0\)
=>x-100=0
=>x=100
(x-1/99+x-99)+(x-3/97+x-7/93)+(x-5/95+x-95/5)=6
a,(x-1/99+x-99)+(x-3/97+x-7/93)+(x-5/95+x-95/5)=6
4+3/5+3/7+...+3/95+3/97+3/99
1/99+1/3*97+1/5*95+..+1/95*5+1/97*3+1/99*1
\(\frac{x-99-1}{99}-\frac{x-99-1}{98}-\frac{x-99-1}{97}-\frac{x-99-1}{96}-\frac{x-99-1}{95}-\frac{x-99-1}{94}\)=0
Ta có :
\(\frac{x-99-1}{99}-\frac{x-99-1}{98}-\frac{x-99-1}{97}-\frac{x-99-1}{96}-\frac{x-99-1}{95}-\frac{x-99-1}{94}=0\)
\(\Leftrightarrow\)\(\frac{x-100}{99}-\frac{x-100}{98}-\frac{x-100}{97}-\frac{x-100}{96}-\frac{x-100}{95}-\frac{x-100}{94}=0\)
\(\Leftrightarrow\)\(\left(x-100\right)\left(\frac{1}{99}-\frac{1}{98}-\frac{1}{97}-\frac{1}{96}-\frac{1}{95}-\frac{1}{94}\right)=0\)
Vì \(\frac{1}{99}-\frac{1}{98}-\frac{1}{97}-\frac{1}{96}-\frac{1}{95}-\frac{1}{94}\ne0\)
Nên \(x-100=0\)
\(\Rightarrow\)\(x=100\)
Vậy \(x=100\)
Bài làm mang tính chất tham khảo vì em mới lớp 7 ~
tính A= (1+1/3+1/5+...+1/95+1/97+1/99) /(1/1*99+1/3*97+1/5*95+...+1/95*5+1/97*3+1/99*1)
Tính :
B = 1 x 3 x 5 - 3 x 5 x 7 + 5 x 7 x 9 - 7 x 9 x 11 + ... + 95 x 97 x 99 - 97 x 99 x 101
E=(1+1/3+1/5+........+1/97+1/99)/(1/1*99+1/3*97+1/5*95+.....+1/97*3+1/99*1)
x+3/97 + x+5/95 + x+4/96 + x+1/99 = -4
\(\frac{x+3}{97}+\frac{x+5}{95}+\frac{x+4}{96}+\frac{x+1}{99}=-4\)
\(\Rightarrow\frac{x+3}{97}+1+\frac{x+5}{95}+1+\frac{x+4}{96}+1+\frac{x+1}{99}+1=0\)
\(\Rightarrow\frac{x+100}{97}+\frac{x+100}{95}+\frac{x+100}{96}+\frac{x+100}{99}=0\)
\(\Rightarrow\left(x+100\right)\left(\frac{1}{97}+\frac{1}{95}+\frac{1}{96}+\frac{1}{99}\right)=0\)
\(\Rightarrow x+100=0\Rightarrow x=-100\)
Vậy x = -100
1+3+5+...+95+97+99=x+100
Số các số hạng:
(99-1):2+1=50 số
Tổng trên là:
(1+99).50:2=2500
=>X+100=2500
=>X=2500-100
=>X=2400
{[99+1].[(99-1):2+1]:2}=x+100
100.50:2=x+100
100.25=x+100
2500=x+100
2500-100=x
2400=x
Vậy x=2400
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