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14 tháng 1 2015

A=1002+2002+3002+...+10002

A=12.1002+22.1002+32.1002+...+102.1002

A=1002.(12+22+32+...+102)

A=10000.385

A=3850000

10 tháng 5 2016

A= 1 +\(\frac{1}{3}\)+\(\frac{1}{6}\)+ .....+ \(\frac{1}{171}\)+\(\frac{1}{190}\)

A= 1 +2.(\(\frac{1}{6}\)+\(\frac{1}{12}\)+....+\(\frac{1}{342}\)+\(\frac{1}{380}\))

A=1+ 2.(\(\frac{1}{2.3}\)+\(\frac{1}{3.4}\)+....+\(\frac{1}{18.19}\)+\(\frac{1}{19.20}\))

A=1+2.(\(\frac{1}{2}\)-\(\frac{1}{3}\)+\(\frac{1}{3}\)-\(\frac{1}{4}\)+......+\(\frac{1}{18}\)-\(\frac{1}{19}\)+\(\frac{1}{19}\)-\(\frac{1}{20}\))

A=1 +2.(\(\frac{1}{2}\)-\(\frac{1}{20}\))

A=1+2.\(\frac{9}{20}\)=1+\(\frac{9}{10}\)=\(\frac{19}{10}\)

10 tháng 5 2016

B=\(\frac{1}{2}\)+\(\frac{1}{2^2}\)+\(\frac{1}{2^3}\)+....+\(\frac{1}{2^{20}}\)

2B= 1 +\(\frac{1}{2}\)+\(\frac{1}{2^2}\)+\(\frac{1}{2^3}\)+......+\(\frac{1}{2^{21}}\)

2B-B= 1-\(\frac{1}{2^{21}}\)

B=1-\(\frac{1}{2^{21}}\)

10 tháng 5 2016

\(A=1+\frac{2}{6}+\frac{2}{12}+...+\frac{2}{380}\)

\(=1+\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{19.20}\)

\(=1+2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{19}-\frac{1}{20}\right)\)

\(=1+2\left(\frac{1}{2}-\frac{1}{20}\right)\)

\(=1+2\times\frac{9}{20}\)

\(=1+\frac{9}{10}\)

\(=\frac{19}{10}\)

b)\(2S=2\left(\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{20}}\right)\)

\(2S=1+\frac{1}{2}+...+\frac{1}{2^{19}}\)

\(2S-S=\left(1+\frac{1}{2}+...+\frac{1}{2^{19}}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{20}}\right)\)

\(S=1-\frac{1}{2^{20}}\)

c)đặt A=1+2+2^2+2^3+...+2^2006+2^2007.

2A=2(1+2+2^2+2^3+...+2^2006+2^2007)

2A=2+2^2+2^3+...+2^2008

2A-A=(2+2^2+2^3+...+2^2008)-(1+2+2^2+2^3+...+2^2006+2^2007)

A=2^2008-1

Giải:

a) S=52/1.6+52/6.11+52/11.16+52/16.21+52/21.26

    S=5.(5.1/6+5/6.11+5/11.16+5/16.21+5/21.26)

    S=5.(1/1-1/6+1/6-1/11+1/11-1/16+1/16-1/21+1/21-1/26)

    S=5.(1/1-1/26)

    S=5.25/26

    S=125/26

b) (1-1/2).(1-1/3).(1-1/4).(1-1/5).....(1-1/19).(1-1/20)

=1/2.2/3.3/4.4/5.....18/19.19/20

=1.2.3.4.....18.19/2.3.4.5.....19.20

=1/20

Chúc bạn học tốt!

5 tháng 5 2021

Cảm ơn bnvui

NV
13 tháng 8 2021

\(S=a+a^3+...+a^{2n+1}\)

\(S.a^2=a^3+a^5+...+a^{2n+1}+a^{2n+3}\)

\(\Rightarrow S\left(a^2-1\right)=a^{2n+3}-a\)

\(\Rightarrow S=\dfrac{a^{2n+3}-a}{a^2-1}\)

\(S_1=1+a^2+...+a^{2n}\)

\(S_1.a^2=a^2+a^4+...+a^{2n}+a^{2n+2}\)

\(\Rightarrow S_1\left(a^2-1\right)=a^{2n+2}-1\)

\(\Rightarrow S_1=\dfrac{a^{2n+2}-1}{a^2-1}\)

21 tháng 12 2021

A. 122

B.256

C.23

21 tháng 12 2021

e: \(=128-\left[68+8\cdot4\right]:4=128-25=103\)

3 tháng 2 2022

a) \(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}\)

=\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}\)

=\(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}\)

=\(1-\dfrac{1}{6}\)=\(\dfrac{5}{6}\)

b) \(\dfrac{1}{15}+\dfrac{1}{35}+\dfrac{1}{63}+\dfrac{1}{99}+\dfrac{1}{143}\)

=\(\dfrac{1}{3.5}+\dfrac{1}{5.7}+\dfrac{1}{7.9}+\dfrac{1}{9.11}+\dfrac{1}{11.13}\)

=\(\dfrac{1.2}{3.5.2}+\dfrac{1.2}{5.7.2}+\dfrac{1.2}{7.9.2}+\dfrac{1.2}{9.11.2}+\dfrac{1.2}{11.13.2}\)

=\(\dfrac{1}{2}\left(\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}+\dfrac{2}{9.11}+\dfrac{2}{11.13}\right)\).

=\(\dfrac{1}{2}\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{13}\right)\)

=\(\dfrac{1}{2}\left(\dfrac{1}{3}-\dfrac{1}{13}\right)\)=\(\dfrac{1}{2}.\dfrac{10}{39}\)=\(\dfrac{5}{39}\).

c) \(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}\)

=\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}\)

=\(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}\)

=\(1-\dfrac{1}{8}=\dfrac{7}{8}\).

d) \(\dfrac{1}{2}+\dfrac{1}{2^2}+\dfrac{1}{2^3}+\dfrac{1}{2^4}+\dfrac{1}{2^5}\)

=\(\dfrac{2^4}{2^5}+\dfrac{2^3}{2^5}+\dfrac{2^2}{2^5}+\dfrac{2}{2^5}+\dfrac{1}{2^5}\)

=\(\dfrac{2^4+2^3+2^2+2+1}{2^5}\)=\(\dfrac{2^5-1}{2^5}=\dfrac{31}{32}\).

e) \(\dfrac{1}{7}+\dfrac{1}{7^2}+\dfrac{1}{7^3}+...+\dfrac{1}{7^{100}}=\dfrac{7^{99}+7^{98}+7^{97}+...+7+1}{7^{100}}=\dfrac{\dfrac{7^{100}-1}{6}}{7^{100}}=\dfrac{7^{100}-1}{6.7^{100}}\)

 

 

=1*200+2*(200-1)+3*(200-2)+...+199(200-198)+200(200-199)

=(1+2+3+...+200)-(1*2+2*3+...+199*200)

=200*201/2-199*200*201/3

=1353400

11 tháng 10

Bài d

a: =(-1)+(-1)+...+(-1)=-1011

b: =(-5)+(-5)+...+(-5)=-175