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Bài 3 :
b) Ta có 1+ 2 + 3 +4 + ...+ x =15
Nên \(\frac{x\left(x+1\right)}{2}=15\)
\(x\left(x+1\right)=30\)
=> \(x\left(x+1\right)=5.6\)
=> x = 5
\(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+.......+\dfrac{1}{x\cdot\left(x+1\right)}=\dfrac{122}{123}\)
\(\Leftrightarrow1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+......+\dfrac{1}{x}-\dfrac{1}{x+1}=\dfrac{122}{123}\)
\(\Leftrightarrow1-\dfrac{1}{x+1}=\dfrac{122}{123}\)
\(\Leftrightarrow\dfrac{1}{x+1}=\dfrac{1}{123}\)
\(\Leftrightarrow x=122\)
\(A=\frac{1}{1x3}+\frac{1}{3x5}+\frac{1}{5x7}+.......\frac{1}{13x15}=\frac{1}{2}x\frac{2}{1x3}+\frac{2}{3x5}.......+\frac{2}{13x15}\)
\(A=\frac{1}{2}x\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}\right)\)
Còn lại em nhân giống ở trên nhé
Đặt A = 1/15 + 1/35 + ... + 1/3135
A = 1/3.5 + 1/5.7 + ... + 1/55.57
2A = 2/3.5 + 2/5.7 + ... + 2/55.57
2A = 1/3 - 1/5 + 1/5 - 1/7 + ... + 1/55 - 1/57
2A = 1/3 - 1/57 = 6/19
A = 3/19
\(a,\left(x+\frac{1}{2}\right)+\left(x+\frac{1}{4}\right)+\left(x+\frac{1}{8}\right)+\left(x+\frac{1}{16}\right)=1\)
\(\Leftrightarrow x+\frac{1}{2}+x+\frac{1}{4}+x+\frac{1}{8}+x+\frac{1}{16}=1\)
\(\Leftrightarrow\left(x+x+x+x\right)+\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}\right)=1\)
\(\Leftrightarrow4\times x+\frac{15}{16}=1\)
\(\Leftrightarrow4\times x=1-\frac{15}{16}\)
\(\Leftrightarrow4\times x=\frac{1}{16}\)
\(\Leftrightarrow x=\frac{1}{16}\div4\)
\(\Leftrightarrow x=\frac{1}{64}\)
\(b,x-\frac{20}{11.13}-\frac{20}{13.15}-...-\frac{20}{53.55}=\frac{3}{11}\)
\(\Leftrightarrow x-\left(\frac{20}{11.13}+\frac{20}{13.15}+...+\frac{20}{53.55}\right)=\frac{3}{11}\)
\(\Leftrightarrow x-\left[715\times\left(\frac{1}{11}-\frac{1}{13}-\frac{1}{13}+...+\frac{1}{55}\right)\right]=\frac{3}{11}\)
\(\Leftrightarrow x-\left[715\times\left(\frac{1}{11}-\frac{1}{55}\right)\right]=\frac{3}{11}\)
\(\Leftrightarrow x-\left[715\times\frac{4}{55}\right]=\frac{3}{11}\)
\(\Leftrightarrow x-52=\frac{3}{11}\)
\(\Leftrightarrow x=\frac{3}{11}+52\)
\(\Leftrightarrow x=\frac{575}{11}\)
Bài 1:
a) 81 + 243 + 319 = 81 + 319 + 243
= 400 + 243 = 643
b) 168 + 1999 + 132 = 168 + 132 + 1999
= 300 + 1999 = 2299
c) 5.25.74.20.4 = (5.20).(25.4).74
= 100.100.74 = 740 000
d) 32.74 + 32.53 = 32.( 74 + 53 )
= 32.127 = 4064
e) 26 + 27 + 28 + 29 + ... + 34 + 35 = (26 + 34) + (27+33) + (28 + 32) + (29 + 31) + 30 + 35
= 60 x 4 + 30 + 35
= 240 + 30 + 35 = 270 + 35 = 305
g) 1 + 3 + 5 + 7 + ... + 99 + 101 = (1 + 99) + (2 + 98) + ... + (48 + 52) + (49 + 51) + 101
= 100 x 49 + 101
= 490 + 101 = 591
Bài 2:
a) 23 - ( 34 - x ) = 23 b) x - ( 74 + 126 ) = 100
34 - x = 23 - 23 74 + 126 = x - 100
34 - x = 0 200 = x - 100
x = 34 - 0 x = 200 - 100
x = 34 x = 100
c) 2436 : x = 12 d) 317 + ( 146 - x ) = 417
x = 2436 : 12 146 - x = 417 - 317
x = 23 146 -x = 100
x = 146 - 100
x = 46
Mình không có thời gian để làm nốt câu e, mong bạn thông cảm!