A=7/1x9 +7/9x17+7/17x25+.....+7/81x89
B=5mũ2/1x4 +3mũ2/4x7+3mũ2+7x10+....+3mũ2/37x40
Ghi các bước tính ra ạ
Biết 7/1x4+ 7/4x7+ 7/7x10+ ⋯ + 7/ 37x40= m/n, trong đó m, n là các số tự nhiên và phân số m/n tối giản.
Tính S = m + n.
\(\dfrac{m}{n}=\dfrac{7}{1\cdot4}+\dfrac{7}{4\cdot7}+...+\dfrac{7}{37\cdot40}\)
\(=\dfrac{7}{3}\left(\dfrac{3}{1\cdot4}+\dfrac{3}{4\cdot7}+...+\dfrac{3}{37\cdot40}\right)\)
\(=\dfrac{7}{3}\left(1-\dfrac{1}{40}\right)\)
\(=\dfrac{7}{3}\cdot\dfrac{39}{40}=\dfrac{91}{40}\)
\(\Leftrightarrow\left(m,n\right)=\left(91;40\right)\)
Suy ra: S=91+40=131
tính nhanh 1/1x4 + 1/4x7 +1/7x10 +...+ 1/37x40
Các bạn giúp mình với
\(A=\dfrac{1}{1\times4}+\dfrac{1}{4\times7}+...+\dfrac{1}{37\times40}\\ =\dfrac{1}{3}\times\left(\dfrac{3}{1\times4}+\dfrac{3}{4\times7}+...+\dfrac{3}{37\times40}\right)\\ =\dfrac{1}{3}\times\left(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{7}+...+\dfrac{1}{37}-\dfrac{1}{40}\right)\\ =\dfrac{1}{3}\times\left(1-\dfrac{1}{40}\right)\\ =\dfrac{1}{3}\times\dfrac{39}{40}\\ =\dfrac{13}{40}\)
Tính tổng : S= 3/1x4 + 3/4x7 + 3/7x10 + ........... + 3/37x40
=1-1/4+1/4-1/7+1/7-...+1/37-1/40
=1-1/40=39/40
a) 2mũ1 nhân 5mũ2 nhân 17
b) 2mũ2 + 2mũ3 + 2mũ4
c) 2mũ5 nhân 3 + 2mũ4 : 8 + 50 : 5mũ2
d) 11mũ2 - 10mũ2 - 3mũ2
e) 1mũ3 + 2mũ3 + 3mũ3 + 4mũ3 + 5mũ3
a, 21.52.17 = 2.25.17 = 50.17 = 850
b, 22 + 23 + 24 = 4 + 8 + 16 = 28
c, 25.3 + 24:8 + 50: 52
= 32.3 + 16:8 + 50:25
=96 + 2 + 2
= 100
d, 112 - 102 - 32
= 121 - 100 - 9
= 21 - 9
= 12
e, 13 + 23 + 33 + 43 + 53
= ( 1+ 2+3+4+5)2
= 152
= 225
thưc hiện phép tính 2/1x4+ 2/ 4x7+2/7x10+...2/37x40
\(\frac{2}{1\times4}+\frac{2}{4\times7}+\frac{2}{7\times10}+...+\frac{2}{37\times40}\)
\(=\frac{2}{3}\times\left(\frac{3}{1\times4}+\frac{3}{4\times7}+\frac{3}{7\times10}+...+\frac{3}{37\times40}\right)\)
\(=\frac{2}{3}\times\left(\frac{4-1}{1\times4}+\frac{7-4}{4\times7}+\frac{10-7}{7\times10}+...+\frac{40-37}{37\times40}\right)\)
\(=\frac{2}{3}\times\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{37}-\frac{1}{40}\right)\)
\(=\frac{2}{3}\times\left(1-\frac{1}{40}\right)=\frac{13}{20}\)
Tính hợp lý và phân tích kết quả đó ra thừa số nguyên tố:
a) 2016mũ0 + 1mũ2016 × (3mũ2 × 3 - 2mũ4:8)
b) 25×29 + 5mũ2 × 2 mũ 2 × 15 + 11×25
A)9mũ2: 3mũ3=
b) 5mũ2 .25mũ 2=
c)1/3mũ2 . 1/9.3mũ2=
Cho mk kết quả nhanh nha
92:33=(32)2:33=34:33=34–3=3
52.252= 52.(52)2=52.54=52+4=56
a)92 : 33 = (32)2 : 33 = 34 : 33 = 3.
b) 52 . 252 = 52 . (52)2 = 52 . 54 = 56.
c) \(\left(\frac{1}{3}\right)^2\) . \(\left(\frac{1}{9.3}\right)^2\) = \(\frac{1^2}{3^2}\). \(\frac{1^2}{27^2}\)= \(\frac{1}{9}\).\(\frac{1}{729}\)= \(\frac{1}{2511}\)
a) \(9^2\div3^3=\left(3^2\right)^2\div3^3=3^4\div3^3=3\)
b) \(5^2\times25^2=5^2\times\left(5^2\right)^2=5^2\times5^4=5^6\)
c) \(\left(\frac{1}{3}\right)^2\times\left(\frac{1}{9\times3}\right)^2=\frac{1^2}{3^2}\times\frac{1^2}{27^2}=\frac{1}{9}\times\frac{1}{729}=\frac{1}{2511}\)
Cho xin cái li ke
3mũ2/1.4+3mũ2/4.7+3mũ2/7.10+.....+3mũ2/67.70
3/3. (3/1.4 + 3/4.7 + 3/7.10 + .... + 3/67.70)=3/3. (1-1/4+1/4-1/7+1/7-1/10+ .... + 1/67-1/70)= 3/3. (1-1/70)=3/3. 69/70 = 207/210=69/70
Rút gọn phân số : (-11).3+7.(-11)/(-15).22; 25.11/15.37-15.48; - 2.3.5mũ2 / 3mũ2. 5mũ3
\(a,\dfrac{\left(-11\right).3+7.\left(-11\right)}{\left(-15\right).22}=\dfrac{\left(-11\right).\left(3+7\right)}{\left(-15\right).22}=\dfrac{-11.10}{-15.22}=\dfrac{-11.2.5}{-11.3.5+2.11}=\dfrac{-1}{-3}=\dfrac{1}{3}\\ \dfrac{25.11}{15.37-15.48}\\ =\dfrac{5.5.11}{15.\left(37-48\right)}=\dfrac{5.5.11}{15.\left(-11\right)}=\dfrac{5.5.11}{3.5.\left(-11\right)}=\dfrac{5}{-3}=-\dfrac{5}{3}\\ \dfrac{-2.3.5^2}{3^2.5^3}=\dfrac{-2}{3.5}=-\dfrac{2}{15}\)
\(\dfrac{\left(-11\right).3+7.\left(-11\right)}{\left(-15\right).22}=\dfrac{-33+\left(-77\right)}{-330}=\dfrac{-110}{-330}=\dfrac{110}{330}=\dfrac{1}{3}\)
\(\dfrac{25.11}{15.37-15.48}=\dfrac{275}{15.\left(37-48\right)}=\dfrac{275}{15.\left(-11\right)}=\dfrac{275}{-165}=-\dfrac{5}{3}\)
\(\dfrac{-2.3.5^2}{3^2.5^3}=\dfrac{-2}{3.5}=-\dfrac{2}{15}\)