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11 tháng 5 2017
S=1-1/4+1-1/9+...+1-1/x2
S=(1+1+1+...+1)-(1/4+1/9+...+1/x2)
Có (1/4+1/9+...+1/x2)<1/(1.2)+1/(2.3)+...+1/(x-1)x=1-1/x<1
=> (1/4+1/9+...+1/x2) ko là số nguyên
=>S ko là số nguyên
U
11 tháng 8 2018
\(A=\frac{-2}{9}+\frac{-3}{4}+\frac{3}{5}+\frac{1}{15}+\frac{1}{57}+\frac{1}{3}+\frac{-1}{36}\)
\(A=\left(\frac{-2}{9}+\frac{-3}{4}+\frac{1}{3}+\frac{-1}{36}\right)+\left(\frac{3}{5}+\frac{1}{15}\right)+\frac{1}{57}\)
\(A=\left(\frac{-8}{36}+\frac{-27}{36}+\frac{12}{36}+\frac{-1}{36}\right)+\left(\frac{9}{15}+\frac{1}{15}\right)+\frac{1}{57}\)
\(A=\frac{-2}{3}+\frac{2}{3}+\frac{1}{57}\)
\(A=\frac{-38}{57}+\frac{38}{57}+\frac{1}{57}\)
\(A=\frac{1}{57}\)
5 tháng 9 2018
\(\frac{x+15}{35}+\frac{x+16}{36}=\frac{x+17}{37}+\frac{x+18}{38}\)
\(\frac{x+15}{35}-1+\frac{x+16}{36}-1=\frac{x+17}{37}-1+\frac{x+18}{38}-1\)
\(\frac{x-20}{35}+\frac{x-20}{36}-\frac{x-20}{37}-\frac{x-20}{38}=0\)
\(\left(x-20\right)\left(\frac{1}{35}+\frac{1}{36}-\frac{1}{37}-\frac{1}{38}\right)=0\)
\(\Rightarrow x-20=0\Rightarrow x=20\)
Vậy x=20
5 tháng 9 2018
\(\frac{x+15}{35}+\frac{x+16}{36}=\frac{x+17}{37}+\frac{x+18}{38}\)
\(\Leftrightarrow\frac{x+15}{35}.885780+\frac{x+16}{36}.885780=\frac{x+17}{37}.885780+\frac{x+18}{38}.885780\)
\(\Leftrightarrow25308\left(x+15\right)+24605\left(x+16\right)=23940\left(x+17\right)+23310\left(x+18\right)\)
\(\Leftrightarrow49913x+773300=47250x+826560\)
\(\Leftrightarrow49913x=47250x+53260\)
\(\Leftrightarrow49913x-47250x=47250x+53260-47250x\)
\(\Leftrightarrow2663x=53260\)
\(\Leftrightarrow x=20\)
\(\Rightarrow x=20\)
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
15 tháng 12 2023
a, (\(\dfrac{9}{10}\) - \(\dfrac{15}{16}\)) \(\times\) ( \(\dfrac{5}{12}\) - \(\dfrac{11}{15}\) - \(\dfrac{7}{20}\))
= (\(\dfrac{72}{80}\) - \(\dfrac{75}{80}\)) \(\times\) (\(\)\(\dfrac{25}{60}\) - \(\dfrac{44}{60}\) - \(\dfrac{21}{60}\))
= - \(\dfrac{3}{80}\) \(\times\) (- \(\dfrac{2}{3}\))
= \(\dfrac{1}{40}\)
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
15 tháng 12 2023
b, (-1)3 + (- \(\dfrac{2}{3}\))2 : 2\(\dfrac{2}{3}\) + \(\dfrac{5}{6}\)
= -13 + \(\dfrac{4}{9}\) : \(\dfrac{8}{3}\) + \(\dfrac{5}{6}\)
= -1 + \(\dfrac{4}{9}\) \(\times\) \(\dfrac{3}{8}\) + \(\dfrac{5}{6}\)
= -1 + \(\dfrac{1}{6}\) + \(\dfrac{5}{6}\)
= -1 + 1
= 0
WC
28 tháng 6 2016
=\(\frac{2x4}{3x3}x\frac{3x5}{4x4}x\frac{4x6}{5x5}x...x\frac{9x11}{10x10}\)
=\(\frac{\left(2x3x4x5x6x..x9\right)x\left(4x5x6x...x11\right)}{\left(3x4x5x6x7x8x9x10\right)x\left(3x4x5x...x10\right)}\)
=\(\frac{2x11}{10x3}=\frac{22}{30}=\frac{11}{15}\)
S
31 tháng 1 2017
25 + 37 - 48 - 25 - 37
= (25 - 25) + (37 - 37) - 48
= 0 + 0 - 48
= -48
2575 + 37 - 2576 - 29
= (2575 - 2576) + (37 - 29)
= -1 + 8 = 7
34 + 35 + 36 + 37 - 14 - 15 - 16 - 17
= (34 - 14) + (35 - 15) + (36 - 16) + (37 - 17)
= 20 + 20 + 20 + 20
= 20 x 4
= 80
21 tháng 7 2018
\(A=\frac{14^{16}-21^{32}.35^{68}}{10^{16}.15^2.7^{96}}=\frac{2^{16}.7^{16}-3^{32}.7^{32}.7^{68}.5^{68}}{5^{16}.2^{16}.3^2.5^2.7^{96}}\)
\(A=\frac{2^{16}.7^{16}-3^{32}.7^{100}.5^{68}}{5^{18}.2^{16}.3^2.7^{96}}=\frac{7^{16}.\left(2^{16}-3^{32}.7^{84}.5^{68}\right)}{5^{18}.2^{16}.3^2.7^{96}}=\frac{2^{16}-3^{32}.7^{84}.5^{68}}{5^{18}.2^{16}.3^2.7^{88}}\)
\(B=\frac{4^{20}-2^{20}+6^{20}}{6^{20}-3^{20}+9^{20}}=\frac{2^{40}-2^{20}+2^{20}.3^{20}}{2^{20}.3^{20}-3^{20}+3^{40}}=\frac{2^{20}.\left(2^{20}-1+3^{20}\right)}{3^{20}.\left(2^{20}-1+3^{20}\right)}\)
\(B=\frac{2^{20}}{3^{20}}\)
LK
0