Question

CMR:

S=\(\frac{1}{5^2}\)-\(\frac{1}{5^4}\)+\(\frac{1}{5^6}\)-.........+\(\frac{1}{5^{4n-2}}\)-\(\frac{1}{5^{4n}}\)+.......+\(\frac{1}{5^{2010}}\)-\(\frac{1}{5^{2012}}\)<\(\frac{1}{26}\)

Answer 1

25S = 1 - 1/5²+1/5⁴- 1/5⁶+.......+1/5²⁰⁰⁸- 1/5²⁰¹⁰

Cộng 2 vế với S ta có :

26S = 1 - 1/5²⁰¹² < 1  suy ra S< 1/26

Answer 2

\(5^2.S=1-\frac{1}{5^2}+\frac{1}{5^4}-.....+\frac{1}{5^{2008}}-\frac{1}{5^{2010}}\)

\(25S=1-\frac{1}{5^2}+\frac{1}{5^4}-...+\frac{1}{5^{2008}}-\frac{1}{5^{2010}}\)Cộng 2 vế với S ta có 

\(26S=1-\frac{1}{5^{2012}}\)\(\Rightarrow26S< 1\Rightarrow S< \frac{1}{26}\)

Answer 3

đăng cho vui, ko cần giải cx đc

Answer 4

           S= \(\frac{1}{5^2}\) -\(\frac{1}{5^4}\) +\(\frac{1}{5^6}\)-.......+ \(\frac{1}{5^{2010}}\)- \(\frac{1}{5^{2012}}\)

\(\Rightarrow\) 5²S= 1- \(\frac{1}{5^2}\) +\(\frac{1}{5^4}\) -..........+\(\frac{1}{5^{2008}}\)- ​​​\(\frac{1}{5^{2010}}\)​

          25S= 1- ​\(\frac{1}{5^2}\)+ \(\frac{1}{5^4}\)-..........+\(\frac{1}{5^{2008}}\)- \(\frac{1}{5^{2010}}\)

\(\Rightarrow\)25S+ S= 1- ​\(\frac{1}{5^2}\)+ \(\frac{1}{5^4}\)-..........+\(\frac{1}{5^{2008}}\)- \(\frac{1}{5^{2010}}\)+ ​\(\frac{1}{5^2}\)​- \(\frac{1}{5^4}\)+​\(\frac{1}{5^6}\)​​-.........+ \(\frac{1}{2^{2010}}\)- \(\frac{1}{5^{2012}}\)

          26S= 1- ​\(\frac{1}{5^{2012}}\)​< 1

​\(\Rightarrow\)​S< \(\frac{1}{26}\)

Answer 5

Trl :

Bạn kia làm đúng rồi nhé !

Học tốt nhé bạn @

Answer 6

1+1= ??? ai biết không