a) i don't know
b) \(\frac{5}{1.2}+\frac{5}{2.3}+\frac{5}{3.4}+...+\frac{5}{28.29}\)
\(5.\left(1-\frac{1}{2}\right)+5.\left(\frac{1}{2}-\frac{1}{3}\right)+5.\left(\frac{1}{3}-\frac{1}{4}\right)+...+5.\left(\frac{1}{28}-\frac{1}{29}\right)\)
\(5.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{28}-\frac{1}{29}\right)\)
\(5.\left(1-\frac{1}{29}\right)\)
\(5.\frac{28}{29}\)
\(\frac{140}{29}\)
c ) \(\frac{4}{2.4}+\frac{4}{4.6}+...+\frac{4}{28.30}\)
\(2.\left(\frac{1}{2}-\frac{1}{4}\right)+2.\left(\frac{1}{4}-\frac{1}{6}\right)+...+2.\left(\frac{1}{28}-\frac{1}{30}\right)\)
\(2.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{28}-\frac{1}{30}\right)\)
\(2.\left(\frac{1}{2}-\frac{1}{30}\right)\)
\(2.\frac{7}{15}=\frac{14}{15}\)
d) đề là thế này nè : 4/6 + 4/12 + 4/20 + 4/30 + 4/42 + 4/56
4/2.3 + 4/3.4 + 4/4.5 + 4/5.6 + 4/6.7 + 4/7.8
4.(1/2-1/3) + 4.(1/3-1/4 ) + 4.(1/4-1/5) + 4.(1/5-1/6 ) + 4.(1/6 - 1/7 ) + 4.(1/7-1/8 )
4.(1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8)
4.(1/2-1/8)
4.1/16
1/4
mình chỉ giải được phần b, c, thôi nhé
b,5/1x2 + 5/2x3 + 5/3x4 +....+5/28x29
=[5/1x2 + 5/2x3 + 5/3x4 +....+ 5/28x29] :5
=5:5/1x2 = 5:5/2x3 + 5:5/3x4 +....+ 5:5/28x29
=1/1x2 + 1/2x3 + 1/3x4 +....+ 1/28x29
Nhận xét :
1/1x2 = 1/1 - 1/2 .....
1/2x3 = 1/2 - 1/3 1/28x29 =1/28 - 1/29
1/3x4 = 1/3 - 1/4
thay vào ta có
=1/1 - 1/2 + 1/2 -1/3 + 1/3 -1/4 +....+ 1/28 - 1/29
=1/1 -1/29
=29/29 - 1/29
=28/29
=28/29 x 5
=140/29
c, 4/2x4 + 4/4x6 +....+ 4/28x30
=[4/2x4 + 4/4x6 + ....+ 4/28x30] :2
=4:2/2x4 + 4:2/4x6 +....+ 4:2/28x30]
=2/2x4 + 2/4x6 +....+ 2/28x30
Nhận xét
2/2x4 = 1/2-1/4 ........
2/4x6 =1/4 -1/6 2/28x30 = 1/28 - 1/30
Thay vào ta có
=1/2 - 1/4 + 1/4 -1/6 +....+ 1/28 + 1/30
=1/2 - 1/30
=15/30 - 1/30
=14/30 x 2
= 14/15
