Question 1146981
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It means that 


    {{{a*(1/2)^1}}} + {{{b*(1/3)^1}}} = {{{5/6}}}      (1)    (at n= 1)

    {{{a*(1/2)^2}}} + {{{b*(1/3)^2}}} = {{{19/36}}}     (2)    (at n= 2)

or

    {{{a*(1/2)}}} + {{{b*(1/3)}}} = {{{5/6}}}       (1')  

    {{{a*(1/4)}}} + {{{b*(1/9)}}} = {{{19/36}}}      (2') 


Now your task is to solve the system (1'), (2') for unknown "a" and "b".

First step, divide by 2 all the terms in equation (1');  keep equation (2') as is.


    {{{a*(1/4)}}} + {{{b*(1/6)}}} = {{{5/12}}}       (3)  

    {{{a*(1/4)}}} + {{{b*(1/9)}}} = {{{19/36}}}       (4) 


Next step subtract equation (4) from equation (3).  You will get then


                     {{{b*(1/6-1/9)}}} = {{{5/12-19/36}}},   or


                     {{{b*(1/18)}}} = {{{-4/36}}} = {{{-2/18}}}

which implies  b = -2.


Then from equation (1) you can find "a".


The rest is just arithmetic, which I leave to you to complete on your own.
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If you still have questions, then let me know.