Question

 

tìm n biết :

\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{n\left(n+3\right)}=\frac{71}{216}\)

Answer 1

Đề bị sai 

Answer 2

Sửa đề . \(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{n\left(n+2\right)}=\frac{71}{216}\)

\(\Leftrightarrow\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{n}-\frac{1}{n+2}\right)=\frac{71}{216}\)

\(\Leftrightarrow\frac{1}{2}.\left(1-\frac{1}{n+2}\right)=\frac{71}{216}\)

\(\Leftrightarrow\frac{1}{n+2}=1-\frac{71}{216}\div\frac{1}{2}\)

\(\Leftrightarrow\frac{1}{n+2}=\frac{37}{108}\)

\(\Leftrightarrow x=\frac{34}{37}\Rightarrow\text{(đề sai) }\)

Answer 3

2(1/1.3+1/3.5+...+1/n(n+2)=2.71/216

2/1.3+2/1.5+...+2/n(n+2)=71/108

1-1/3+1/3-1/5+1/5-...-1/n+1/n+2=71/108

1-1/n+2=71/108

n+1/n+2=71/108

n=........

Answer 4

Ta có : \(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+.....+\frac{1}{n\left(n+3\right)}=\frac{71}{216}\)

\(\Rightarrow\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+.....+\frac{2}{n\left(n+3\right)}=\frac{71}{108}\)

\(\Rightarrow1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+.....+\frac{1}{n}-\frac{1}{n+3}=\frac{71}{108}\)

\(\Rightarrow1-\frac{1}{n+3}=\frac{71}{108}\)

\(\Rightarrow\frac{n+2}{n+3}=\frac{71}{108}\)

=> 108n + 216 = 71n + 213

=> 108n - 71n = 213 - 216

=> 37n = -3

=> n = -3/37

Answer 5

Đề sai rồi em ơi
 

Answer 6

\(\frac{1}{1.3}\)+ \(\frac{1}{3.5}\)+ \(\frac{1}{5.7}\)+...+ \(\frac{1}{n.\left(n+3\right)}\)= \(\frac{71}{216}\)

= 1- \(\frac{1}{3}\)+ \(\frac{1}{3}\)- \(\frac{1}{5}\)+...+ \(\frac{1}{n}\)- \(\frac{1}{n+3}\)= \(\frac{71}{216}\)

=1- \(\frac{1}{n+3}\)                                                  = \(\frac{71}{216}\)

= n +1                                                              = \(\frac{71}{216}\)

 n                                                                    = \(\frac{71}{216}\)- 1

 n                                                                   = \(\frac{-145}{216}\)

^-^ mik cũng ko chắc chắn là đúng đâu nha