\(A=\dfrac{9}{8}-\dfrac{8}{9}+\dfrac{3}{24}+\dfrac{1}{4}-\dfrac{5}{16}+\dfrac{19}{25}-\dfrac{1}{9}+\dfrac{2}{25}-\dfrac{1}{81}\)

\(=\dfrac{9}{8}+\dfrac{1}{4}-\dfrac{5}{16}+\dfrac{1}{8}-\dfrac{8}{9}-\dfrac{1}{9}-\dfrac{1}{81}+\dfrac{19}{25}+\dfrac{2}{25}\)

\(=\dfrac{10}{8}+\dfrac{1}{4}-\dfrac{5}{16}-1-\dfrac{1}{81}+\dfrac{21}{25}\)

\(=\dfrac{20+4-5}{16}-\dfrac{82}{81}+\dfrac{21}{25}\)

\(=\dfrac{19}{16}-\dfrac{82}{81}+\dfrac{21}{25}\)

\(=\dfrac{32891}{16\cdot81\cdot25}\)

b: \(B=-\dfrac{1}{3}-\dfrac{8}{35}-\dfrac{2}{9}-\dfrac{1}{35}+\dfrac{4}{5}-\dfrac{4}{9}+\dfrac{3}{7}\)

\(=\dfrac{-1}{3}-\dfrac{2}{9}-\dfrac{4}{9}-\dfrac{8}{35}-\dfrac{1}{35}+\dfrac{4}{5}+\dfrac{3}{7}\)

\(=\dfrac{-3-2-4}{9}+\dfrac{-9}{35}+\dfrac{28+15}{35}\)

\(=-1+\dfrac{-9+43}{35}=-1+\dfrac{34}{35}=-\dfrac{1}{35}\)

a) \(S=1^5+3^5+....+75^5+99^5\)

\(\left(2a+1\right)^5-\left(2a+1\right)=2a\left(2a+1\right)\left(2a+2\right)\left[\left(2a+1\right)^2+1\right]\)

\(\left(2a+1\right)^5-\left(2a+1\right)=4a\left(2a+1\right)\left(a+1\right)\left[\left(2a+1\right)^2+1\right]⋮4\)

\(S=\left(1^5-1\right)+\left(3^5-3\right)+....+\left(75^5-75\right)+\left(99^5-99\right)+\left(1+3+5+...+75+99\right)\)

\(\Leftrightarrow\begin{matrix}1^5-1⋮4\\3^5-3⋮4\\5^5-5⋮4\\...........\\75^5-5⋮4\\99^5-99⋮4\end{matrix}\)

\(S_1=1+3+5+7+...+75+99=\frac{\left(1+75\right)\left[\frac{75-1}{2}+1\right]}{2}+99=38.38+96+3\)

\(\Rightarrow S_1:4\) dư 3

\(\Leftrightarrow S\) chia 4 dư 3

a)  \(35\times17+84\times35-35\)

\(=35\times\left(17+84-1\right)\)

\(=35\times100=3500\)

b)  \(\frac{5}{2}\times\frac{1}{3}-\frac{1}{4}=\frac{5}{6}-\frac{1}{4}=\frac{7}{12}\)

c)  \(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right).....\left(1-\frac{1}{2017}\right)\left(1-\frac{1}{2018}\right)\)

\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.....\frac{2016}{2017}.\frac{2017}{2018}\)

\(=\frac{1}{2018}\)

a)35x17+84x35-35

=35x(17+84-1)

=35x100

=3500

b)5/2x1/3-1/4

=5/6-1/4

=7/12

c)(1-1/2)x(1-1/3)x(1-1/4)x......x(1-1/2018)

=1/2x2/3x3/4x...x2017/2018

=1/2018

bạn cứ chép thế ko hiểu thì thôi

a,

\(35\times17+84\times35-35.\)

\(=35\times17+84\times35-35\times1\)

   = 35 x ( 17 + 84 - 1)

    = 35 x 100

     =3500

b, 

5/2 x 1/3 - 1/4

= 5/6 - 1/4

= 7/12

a) (27 -18) : 3 =?

Cách 1: (27 -18) : 3

= 9 : 3 = 3

Cách 2:(27 -18) : 3

= 27 : 3 - 18 : 3

= 9 - 6 = 3

b) (64 - 32) : 8 = ?

Cách 1:(64 - 32) : 8

= 32 : 8 = 4

Cách 2:(64 - 32) : 8

= 64 : 8 - 32 : 8

= 8 - 4 = 4

Nói thêm: Khi chia một hiệu cho một số, ta có thể chia số bị trừ và số trừ cho số đó (nếu chia hết), rồi trừ hai kết quả cho nhau.

(27 -18) : 3

= 27 : 3 - 18 : 3

a)\(A=\frac{1}{15}+\frac{1}{35}+...+\frac{1}{195}=\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{13.15}=\frac{1}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{13}-\frac{1}{15}\right)=\frac{1}{2}\left(\frac{1}{3}-\frac{1}{15}\right)=\frac{2}{15}\)

b)\(M=1+3+3^2+...+3^{25}=\frac{3^{26}-1}{3-1}=\frac{3^{26}-1}{2}

bạn đọc lại đề bài b) đi

A=3+32+33+34+...+325A=3+32+33+34+...+325

→A=(3+32+33+34+35)+(36+37+38+39+310)+...+(321+322+323+324+325)→A=(3+32+33+34+35)+(36+37+38+39+310)+...+(321+322+323+324+325)

→A=3(1+3+32+33+34)+36(1+3+32+33+34)+...+321(1+3+32+33+34)→A=3(1+3+32+33+34)+36(1+3+32+33+34)+...+321(1+3+32+33+34)

→A=(1+3+32+33+34)(3+36+...+321)→A=(1+3+32+33+34)(3+36+...+321)

→A=40(3+36+...+321)→A=40(3+36+...+321)

→A⋮40

A = 1 + 3 + 3² + 3³ + 3⁴ + 3⁵ + 3⁶ + 3⁷ + .... + 3³² + 3³³ + 3³⁴ + 3³⁵

    = (1 + 3 + 3² + 3³) + (3⁴ + 3⁵ + 3⁶ + 3⁷) + .... + (3³² + 3³³ + 3³⁴ + 3³⁵) 

    = (1 + 3 + 3² + 3³) + 3⁴.(1 + 3 + 3² + 3³) +.... + 3³².(1 + 3 + 3² + 3³) 

    = 40 + 3⁴.40 + ... + 3³².40

    = 40.(1 + 3⁴ + .... + 3³²) \(⋮\)40

=> A chia 4 dư 0

quá dễ 

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