Question

Se considera șirul de fracti 1/2;3/4;5/6;
B)Scrieti fractia care se afla pe locul 50 în șir
C)Scrieti fractia care se afla pe locul n-1 in sir
/ supra
dau 100p
plus coroana​

Answer 1

Răspuns:

$\it a)~~\boxed{\boxed{\dfrac{7}{8};~\dfrac{9}{10};~\dfrac{11}{12};~\dfrac{13}{14};.....}}$

$\it b)~~\boxed{\boxed{\it T_{50} =\dfrac{99}{100}}}$

$\it c)~~ \boxed{\boxed{\it T_{n-1} =\dfrac{2n-3}{2n-2}}}$

Explicație pas cu pas:

(◡‿◡) Salutare!

$\it~~~~~~~~~~~$

$\it \dfrac{1}{2};~\dfrac{3}{4};~ \dfrac{5}{6}; .......................$

$\it~~~~~~~~~$

$\it T_{1} =\dfrac{1}{2}~\xrightarrow[a~termenului]{alta~scriere}~T_{1} = \dfrac{2\cdot 1 - 1}{2\cdot 1}$

$\it T_{2} =\dfrac{3}{4}~\xrightarrow[a~termenului]{alta~scriere}~T_{2} = \dfrac{ 2\cdot2-1}{2\cdot2}$

$\it T_{3} =\dfrac{5}{6}~\xrightarrow[a~termenului]{alta~scriere}~T_{3} = \dfrac{ 2\cdot3-1}{2\cdot3}$

$\it T_{4} =\dfrac{7}{8}~\xrightarrow[a~termenului]{alta~scriere}~T_{4} = \dfrac{ 2\cdot4-1}{2\cdot4}$

$\it T_{5} =\dfrac{9}{10}~\xrightarrow[a~termenului]{alta~scriere}~T_{5} = \dfrac{ 2\cdot5-1}{2\cdot5}$

$\it T_{6} =\dfrac{11}{12}~\xrightarrow[a~termenului]{alta~scriere}~T_{6} = \dfrac{ 2\cdot6-1}{2\cdot 6}$

$\it T_{7} =\dfrac{13}{14}~\xrightarrow[a~termenului]{alta~scriere}~T_{7} = \dfrac{ 2\cdot7-1}{2\cdot 7}$

$\it T_{8} =\dfrac{15}{16}~\xrightarrow[a~termenului]{alta~scriere}~T_{8} = \dfrac{ 2\cdot8-1}{2\cdot 8}$

$\it..............................................$

$\boxed{\boxed{\it T_{n} = \dfrac{2\cdot n-1}{2\cdot n}\rightarrow forma~termenului~general}}$

$\it T_{50} = \dfrac{2\cdot 50-1}{2\cdot 50}\implies T_{50} = \dfrac{100-1}{100}\implies \boxed{\boxed{\it T_{50} =\dfrac{99}{100}}}$

$\it T_{n-1} = \dfrac{2\cdot (n-1)-1}{2\cdot (n-1)}\implies T_{n-1} = \dfrac{2n-2-1}{2n-2}\implies \boxed{\boxed{\it T_{n-1} =\dfrac{2n-3}{2n-2}}}$

#copaceibrainly