Cho C= \(\frac{7}{3^2.4^2}+\frac{9}{4^2.5^2}+\frac{11}{5^2.6^2}+.....\frac{29}{14^2.15^2}\)
CMR: C<\(\frac{1}{5}\)
Những câu hỏi liên quan
\(\frac{11^4.6-11^5}{11^4-11^5}:\frac{9^8.3-9^9}{9^8.5+9^8.7}\)
\(\frac{3}{5}:\left(\frac{-1}{5}-\frac{1}{6}\right)+\frac{3}{5}:\left(\frac{-1}{3}-1\frac{1}{15}\right)\)
\(\left(\frac{1}{2}-\frac{13}{14}\right):\frac{5}{7}-\left(-\frac{2}{21}+\frac{1}{7}\right):\frac{5}{7}\)
\(\frac{4^5.9^4-2.6^9}{2^{10}.3^8+6^8.20}\)
a)\(\frac{11^4.6-11^5}{11^4-11^5}:\frac{9^8.3-9^9}{9^8.5+9^8.7}\)
\(=1.6:\frac{9^8.3-9^8.9}{9^8.\left(5+7\right)}\)
\(=6:\frac{9^8.\left(3-9\right)}{9^8.12}\)
\(=6:\frac{9^8.\left(-6\right)}{9^8.12}\)
\(=6:\left(-\frac{6}{12}\right)\)
\(=6:\left(-\frac{1}{2}\right)\)
\(=-12\)
b) 3/5 : ( -1/5-1/6)+3/5:(-1/3-16/15) ( mình chuyển về ps luôn )
=3/5: (-11/30) + 3/5 : (-7/5)
=3/5:[-11/30+(-7/5)]
=3/5:53/30
=18/53
c) (1/2-13/14):5/7-(-2/21+1/7):5/7
= -3/7:5/7-1/21:5/7
=(-3/7-1/21):5/7
=-10/21:5/7
=-2/3
câu b vá c mình làm tắt nha. chúc bạn học tốt
Đúng 0
Bình luận (0)
Tính giá trị biểu thứca,Afrac{24cdot47-23}{24+47-23}cdotfrac{3+frac{3}{7}-frac{3}{11}+frac{3}{1001}-frac{3}{13}}{frac{9}{1001}-frac{9}{13}+frac{9}{7}-frac{9}{11}+9}b,Mfrac{1+2+2^2+2^3+...+2^{2012}}{2^{2014}-2}c,A81cdotleft[frac{12-frac{12}{7}-frac{12}{289}-frac{12}{85}}{4-frac{4}{7}-frac{4}{289}-frac{4}{85}}:frac{5+frac{5}{13}+frac{5}{169}+frac{5}{91}}{6+frac{6}{13}+frac{6}{169}+frac{6}{91}}right]:frac{158158158}{711711711}d,Afrac{5cdotleft(2^2.3^2right)^9cdotleft(2^2right)^6-2cdotleft(2^2cdot3r...
Đọc tiếp
Tính giá trị biểu thức
a,\(A=\frac{24\cdot47-23}{24+47-23}\cdot\frac{3+\frac{3}{7}-\frac{3}{11}+\frac{3}{1001}-\frac{3}{13}}{\frac{9}{1001}-\frac{9}{13}+\frac{9}{7}-\frac{9}{11}+9}\)
b,\(M=\frac{1+2+2^2+2^3+...+2^{2012}}{2^{2014}-2}\)
c,\(A=81\cdot\left[\frac{12-\frac{12}{7}-\frac{12}{289}-\frac{12}{85}}{4-\frac{4}{7}-\frac{4}{289}-\frac{4}{85}}:\frac{5+\frac{5}{13}+\frac{5}{169}+\frac{5}{91}}{6+\frac{6}{13}+\frac{6}{169}+\frac{6}{91}}\right]:\frac{158158158}{711711711}\)
d,\(A=\frac{5\cdot\left(2^2.3^2\right)^9\cdot\left(2^2\right)^6-2\cdot\left(2^2\cdot3\right)^{14}\cdot3^4}{5\cdot2^{28}\cdot3^{18}-7\cdot2^{29}\cdot3^{18}}\)
Cho C = \(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{99}}\)chứng minh rằng C < \(\frac{1}{2}\)CMR : \(\frac{3}{1^2.2^2}+\frac{5}{2^2.3^2}+\frac{7}{3^2.4^2}+...+\frac{19}{9^2.10^2}< 1\)CMR : \(\frac{1}{3}+\frac{2}{3^2}+\frac{3}{3^3}+\frac{4}{3^4}+...+\frac{100}{3^{100}}< \frac{3}{4}\)
Xem chi tiết
#)Giải :
Bài 1 :
\(C=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{99}}\Leftrightarrow3C=1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{100}}\)
\(\Leftrightarrow3C-C=\left(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{100}}\right)-\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{99}}\right)\)
\(\Leftrightarrow2C=1-\frac{1}{3^{100}}\Leftrightarrow C=\frac{1-\frac{1}{3^{100}}}{2}< \frac{1}{2}\Rightarrow C< \frac{1}{2}\left(đpcm\right)\)
Bài 2 :
\(\frac{3}{1^2.2^2}+\frac{5}{2^2.3^2}+\frac{7}{3^2.4^2}+...+\frac{19}{9^2.10^2}=\frac{3}{1.4}+\frac{5}{4.9}+\frac{7}{9.16}+...+\frac{19}{81.100}\)
\(=\left(1-\frac{1}{4}\right)+\left(\frac{1}{4}-\frac{1}{9}\right)+\left(\frac{1}{9}-\frac{1}{16}\right)+...+\left(\frac{1}{81}-\frac{1}{100}\right)=1-\frac{1}{100}=\frac{99}{100}< 1\)
\(\Rightarrow\frac{3}{1^2.2^2}+\frac{5}{2^2.3^2}+\frac{7}{3^2.4^2}+...+\frac{19}{9^2.10^2}< 1\left(đpcm\right)\)
Đúng 0
Bình luận (0)
tính tổng
\(A=\frac{1}{1.2}+\frac{2}{1.3}+\frac{3}{2.5}+\frac{5}{3.8}+\frac{8}{5.13}+\frac{13}{8.21}+...+\frac{987}{610.1597}\)
\(B=\frac{2^2}{1.3}+\frac{3^2}{2.4}+\frac{4^2}{3.5}+...+\frac{2017^2}{2016.2018}\)
\(C=\frac{5}{1.2.3}+\frac{8}{2.3.4}+\frac{11}{3.4.5}+...+\frac{6025}{2011.2012.2013}\)
bạn phải cho ra 2 số cuối thì mới làm đc nha có 1 s
ố cuối ko làm đc đâu
Đúng 0
Bình luận (0)
A= 1-1/2 + 1-1/3 + 1/2-1/5 + 1/3-1/8+ 1/5-1/13+1/8- 1/21 +....+ 1/610- 1/1597
A= 1/610
Đúng 0
Bình luận (0)
1/610 nha bn
k giùm mk nha các bn
>_< học tốt
Đúng 0
Bình luận (0)
Xem thêm câu trả lời
Tính hợp lí:
a, 75. ( -2frac{3}{25}+7frac{2}{75}-5frac{4}{15} )
b, 45.left(5frac{4}{15}-4frac{7}{9}-1frac{8}{45}right)
c, frac{-5}{8}+frac{14}{18}-frac{3}{8}+frac{2}{9}-frac{1}{2006}
d, frac{15}{29}-frac{8}{7}+frac{16}{14}+frac{14}{29}-frac{3}{8}
e, frac{1}{3.5}+frac{1}{5.7}+...+frac{1}{49.51}
Đọc tiếp
Tính hợp lí:
a, 75. ( \(-2\frac{3}{25}+7\frac{2}{75}-5\frac{4}{15}\) )
b, \(45.\left(5\frac{4}{15}-4\frac{7}{9}-1\frac{8}{45}\right)\)
c, \(\frac{-5}{8}+\frac{14}{18}-\frac{3}{8}+\frac{2}{9}-\frac{1}{2006}\)
d, \(\frac{15}{29}-\frac{8}{7}+\frac{16}{14}+\frac{14}{29}-\frac{3}{8}\)
e, \(\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{49.51}\)
tính giá trị các biểu thức sauAfrac{4^6.9^5+6^9.120}{-8^4.3^{12}+6^{11}} Bfrac{5.left(2^2.3^2right)^9.left(2^2right)^6-2.left(2^2.3right)^{14}.3^{4.}}{5^2.2^{28}.3^{18}-7.2^{29}.3^{18}}Cfrac{5^2.6^{11}.6^{12}+6^2.12^6.15^2}{2.6^{12}.10^4+81^2.960^3} Dfrac{11.3^{22}.3^2-9^{15}}{left(2.3^{14}right)^2}
Đọc tiếp
tính giá trị các biểu thức sau
\(A=\frac{4^6.9^5+6^9.120}{-8^4.3^{12}+6^{11}}\) \(B=\frac{5.\left(2^2.3^2\right)^9.\left(2^2\right)^6-2.\left(2^2.3\right)^{14}.3^{4.}}{5^2.2^{28}.3^{18}-7.2^{29}.3^{18}}\)
\(C=\frac{5^2.6^{11}.6^{12}+6^2.12^6.15^2}{2.6^{12}.10^4+81^2.960^3}\) \(D=\frac{11.3^{22}.3^2-9^{15}}{\left(2.3^{14}\right)^2}\)
tính:a.\(2^6.5^6\)b.\(8^2.5^2\)c.\(4^3.5^3\)d.\(5^2.6^2.3^2\)e.\(\frac{625^5}{25^8}\)g.\(\frac{3^9}{7}.\frac{7^9}{3}\)
giúp mình nha các bạn !
a , 106 b , 402 c 203 d,902 e , 54 g , 218
Đúng 0
Bình luận (0)
#)Giải :
a)\(2^6.5^6=\left(2.5\right)^6=10^6\)
b)\(8^2.5^2=\left(8.5\right)^2=40^2\)
c)\(4^3.5^3=\left(4.5\right)^3=20^3\)
d)\(5^2.6^2.3^2=\left(5.6.2\right)^2=60^2\)
e)\(\frac{625^5}{25^8}=\frac{\left(25^2\right)^5}{25^8}=\frac{25^{10}}{25^8}=25^2\)
g)\(\frac{3^9}{7}.\frac{7^9}{3}=\frac{\left(3.7\right)^9}{7.3}=\frac{21^9}{21}=21^8\)
Đúng 0
Bình luận (0)
a) 26 . 56 = (2.5)6 = 106
b) 82.52 = (8.5)2 = 402
c) 43.53 = (4.5)3 = 203
d) 52.62.32 = (5.6.2)2 = 602
e) \(\frac{625^5}{25^8}=\frac{\left(25^2\right)^5}{25^8}=\frac{25^{2.5}}{25^8}=\frac{25^{10}}{25^8}=\frac{25^8.25^2}{25^8}=25^2=625\)
g) \(\frac{3^9}{7}.\frac{7^9}{3}=\frac{3^9.7^9}{7.3}=\frac{\left(7.3\right)^9}{7.3}=\frac{21^9}{21}=21^8\)
Đúng 0
Bình luận (0)
Xem thêm câu trả lời
a,frac{4^5.9^4-2.6^9}{2^{10}.3^8+6^8.20}
b,frac{27^2.8^5}{6^6.32^3}+frac{3^4.4^4}{2^2.6^2}
c,left(1+frac{1}{1.3}right)left(1+frac{1}{2.4}right)left(1+frac{1}{3.5}right)........left(1+frac{1}{20.22}right)
d,frac{3}{2}+frac{7}{6}+frac{13}{12}+frac{21}{20}+.....+frac{91}{90}
e,left(-2^2right)+sqrt{36}-sqrt{9}+sqrt{25} 20).20)
Đọc tiếp
a,\(\frac{4^5.9^4-2.6^9}{2^{10}.3^8+6^8.20}\)
b,\(\frac{27^2.8^5}{6^6.32^3}+\frac{3^4.4^4}{2^2.6^2}\)
c,\(\left(1+\frac{1}{1.3}\right)\)\(\left(1+\frac{1}{2.4}\right)\)\(\left(1+\frac{1}{3.5}\right)\)........\(\left(1+\frac{1}{20.22}\right)\)
d,\(\frac{3}{2}\)+\(\frac{7}{6}\)+\(\frac{13}{12}+\frac{21}{20}+.....+\frac{91}{90}\)
e,\(\left(-2^2\right)+\sqrt{36}-\sqrt{9}+\sqrt{25}\) 20).20)
Tính nhanh:
a/\(\left(2+\frac{-7}{13}\right)+\frac{-6}{13}\)
b/\(\frac{-5}{11}+\left(\frac{2}{3}+\frac{-6}{11}\right)\)
c/\(\frac{5}{9}+\frac{-7}{11}+\frac{9}{29}+\frac{4}{9}+\frac{-4}{11}\)
Tính nhanh :
a)
\(\left(2+\frac{-7}{13}\right)+\frac{-6}{13}\)
= \(2+\left(\frac{-7}{13}+\frac{-6}{13}\right)\)
= \(2+\frac{-13}{13}=2+\left(-1\right)\)
= 1
tk mk nha
chắc chắn đúng luôn ấy
mk đang âm rất nhiều này ! huhuhu giúp nha
Đúng 0
Bình luận (0)
a)=1
b)=\(-\frac{1}{3}\)
c)=\(\frac{9}{29}\)
Đúng 0
Bình luận (0)
a) \(\left(2+\frac{-7}{13}\right)+\frac{-6}{13}\)
\(=2+\frac{-7}{13}+\frac{-6}{13}\)
\(=2+-1\)
\(=1\)
b) \(\frac{-5}{11}+\left(\frac{2}{3}+\frac{-6}{11}\right)\)
\(=\frac{-5}{11}+\frac{-6}{11}+\frac{2}{3}\)
\(=-1+\frac{2}{3}\)
\(=-\frac{1}{3}\)
c) \(\frac{5}{9}+\frac{-7}{11}+\frac{9}{29}+\frac{4}{9}+\frac{-4}{11}\)
\(=\frac{5}{9}+\frac{4}{9}+\frac{-7}{11}+\frac{-4}{11}+\frac{9}{29}\)
\(=1+-1+\frac{9}{29}\)
\(=0+\frac{9}{29}\)
\(=\frac{9}{29}\)
Đúng 0
Bình luận (0)
Xem thêm câu trả lời