a)\(2S=2\left(1+\frac{1}{2}+...+\frac{1}{2^{100}}\right)\)

\(2S=2+1+...+\frac{1}{2^{99}}\)

\(2S-S=\left(2+1+...+\frac{1}{2^{99}}\right)-\left(1+\frac{1}{2}+...+\frac{1}{2^{100}}\right)\)

\(S=2-\frac{1}{2^{100}}\)

phần b tương tự

a. S=1+1/2+1/2^2+1/2^3+...+1/2^100

2S=2+1+1/2+1/2^2+...+1/2^99

2S-S=(2+1+1/2+1/2^2+...+1/2^99)-(1+1/2+1/2^2+1/2^3+...+1/2^100)

S=2-1/2^100

S=2^101-1/2^100

\(S=1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^7}\)

\(3S=3+1+\frac{1}{3}+...+\frac{1}{3^6}\)

\(3S-S=\left(3+1+\frac{1}{3}+...+\frac{1}{3^6}\right)-\left(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^7}\right)\)

\(2S=3-\frac{1}{3^7}\)

\(S=\frac{3-\frac{1}{3^7}}{2}\)

S= 1+ \(\frac{1}{3}\)+ \(\frac{1}{9}\)+...+ \(\frac{1}{729}\)+ \(\frac{1}{2187}\).

=> S= 1+ \(\frac{1}{3}\)+ \(\frac{1}{3^2}\)+...+ \(\frac{1}{3^6}\)+ \(\frac{1}{3^7}\).

=>3S= 3+ 1+ \(\frac{1}{3}\)+...+ \(\frac{1}{3^5}\)+ \(\frac{1}{3^6}\).

=> 3S- S=( 3+ 1+ \(\frac{1}{3}\)+...+ \(\frac{1}{3^5}\)+ \(\frac{1}{3^6}\))-( 1+ \(\frac{1}{3}\)+ \(\frac{1}{3^2}\)+...+ \(\frac{1}{3^6}\)+ \(\frac{1}{3^7}\)).

=> 2S= 3- \(\frac{1}{3^7}\).

=> 2S= 3- \(\frac{1}{2187}\).

=> 2S= \(\frac{6560}{2187}\).

=> S= \(\frac{6560}{2187}\): 2.

=> S= \(\frac{3280}{2187}\).

Vậy S= \(\frac{3280}{2187}\).

S=1+5+5^2+5^3+..+5^2016

5S=5(1+5+5^2+5^3+..+5^2016)

5S=5+5^2+5^3+5^4+..+5^2017

=>5S-S=(5+5^2+5^3+5^4+..+5^2017)-(1+5+5^2+5^3+...+5^2016)

4S=5^2017-1

S=(5^2017-1)/4

5S=5+5^2+5^3+...+5^2017

4S=(5+5^2+5^3+...+5^2017)-(1+5+5^2+...+5^2016)

4S=5^2017-1(cho này hơi khó hiểu bạn nên đoc kì lại)

S=5^2017-1

         4

B =1+3+3²+3³+.....+3²⁰¹⁶

3.B=3.(1+3+3²+3³+.....+3²⁰¹⁶⁾

3.B=   3+3²+3³+.....+3²⁰¹⁷ 

_

   B=1+3+3²+3³+.....+3²⁰¹⁶

2.B=3²⁰¹⁷-1                B=3²⁰¹⁷-1 :2

vậy kết quả là bao nhiêu vậy bạn

là số có mấy chữ số

\(1\frac{13}{15}.0,75-\left(\frac{104}{195}+25\%\right).\frac{24}{47}-3\frac{12}{13}:3\)

\(=\frac{28}{15}.\frac{3}{4}-\left(\frac{8}{15}+\frac{1}{4}\right).\frac{8}{9}-\frac{51}{13}.\frac{1}{3}\)

\(=\frac{7}{5}-\left(\frac{32}{60}+\frac{15}{60}\right).\frac{8}{9}-\frac{17}{13}\)

\(=\frac{7}{5}-\frac{47}{60}.\frac{8}{9}-\frac{17}{13}\)

\(=\frac{7}{5}-\frac{94}{135}-\frac{17}{13}\)

\(=\frac{-212}{351}\)

Tự quy đồng

\(2\frac{3}{4}.\left(-0,4\right)-1\frac{3}{5}.2,75+\left(-1,2\right):\frac{4}{11}\)

\(=\frac{11}{4}.\frac{-2}{5}-\frac{8}{5}.\frac{11}{4}-\frac{6}{5}.\frac{11}{4}\)

\(=\frac{11}{4}.\left(\frac{-2}{5}-\frac{8}{5}-\frac{6}{5}\right)\)

\(=\frac{11}{4}.\frac{-16}{5}\)

\(=\frac{-44}{5}=-8\frac{4}{5}\)

\(\frac{3-\frac{1}{2}+\frac{1}{4}}{\frac{2}{3}-\frac{5}{6}-\frac{3}{4}}=\frac{\left(3-\frac{1}{2}+\frac{1}{4}\right)\left(3.4\right)}{\left(\frac{2}{3}-\frac{5}{6}-\frac{3}{4}\right)\left(3.4\right)}=\frac{36-6+3}{8-10-9}=\frac{33}{-11}=-3\)