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\(A=\frac{2}{1.4}+\frac{2}{4.7}+\frac{2}{7.10}+...+\frac{2}{97.100}\)
\(A=2\left(\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{97.100}\right)\)
\(A=2\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{97}-\frac{1}{100}\right)\)
\(A=2\left(1-\frac{1}{100}\right)\)
\(A=2.\frac{99}{100}=..............\)
Tự làm nốt nha
=2/3(3/1*4+3/4*7+...+3/97*100)
=2/3(1-1/4+1/4-1/7+...+1/97-1/100)
=2/3*99/100
=198/300
=66/100
=33/50
\(\dfrac{3}{1.4}+\dfrac{3}{4.7}+\dfrac{3}{7.10}+...+\dfrac{3}{27.30}\)
\(=1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{10}+...+\dfrac{1}{27}-\dfrac{1}{30}\)
\(=1-\dfrac{1}{30}\)
\(=\dfrac{29}{30}\)
Chúc bạn học tốt
A= 3/1.4+ 3/4.7+ 3/7.10+...+ 3/27.30
= 1/3 . ( 3- 3/4 + 3/4- 3/7 +3/7- 3/10+... + 3/27- 3/30)
= 1/3 . (3 - 3/30)= 1/3 . 87/30= 87/90=29/30
A = \(\dfrac{15}{1.4}\) + \(\dfrac{15}{4.7}\) + \(\dfrac{15}{7.10}\) + ... + \(\dfrac{15}{61.64}\)
A = \(5.\left(\dfrac{3}{1.4}+\dfrac{3}{4.7}+\dfrac{3}{7.10}...+\dfrac{3}{61.64}\right)\)
A = 5.( \(\dfrac{1}{1}\) - \(\dfrac{1}{4}\) + \(\dfrac{1}{4}\) - \(\dfrac{1}{7}\) + \(\dfrac{1}{7}\) - \(\dfrac{1}{10}\) + ... + \(\dfrac{1}{61}\) - \(\dfrac{1}{64}\))
A = 5.( \(\dfrac{1}{1}\) - \(\dfrac{1}{64}\))
A = 5. \(\dfrac{63}{64}\)
A = \(\dfrac{315}{64}\)
A = 1/1 -1/4 +1/4 - 1/7 +1/7 ........+1/40 - 1/43
A = 1/1 - 1/43
A = 42/43
A=1 - 1/4 + 1/4 - 1/7 + .... + 1/40 - 1/43
= 1 - 1/43
= 42/43