SOLUTION: The n^th term, tn of a series:5/6+19/36+65/216+....... is given by Tn=a(1/2)^n+b(1/3)^n: find the values of a and b

Algebra ->  Sequences-and-series -> SOLUTION: The n^th term, tn of a series:5/6+19/36+65/216+....... is given by Tn=a(1/2)^n+b(1/3)^n: find the values of a and b       Log On


   

Question 1146981: The n^th term, tn of a series:5/6+19/36+65/216+....... is given by Tn=a(1/2)^n+b(1/3)^n: find the values of a and b

Found 2 solutions by richwmiller, ikleyn:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
In math, tn, TN and Tn are three different and distinct variables.
pseudo tutor maththerapy is not a tutor. He might know some math but he is not a teacher.
Tutor Ikleyn, if you mean you intend to present your case to Igor, go right ahead.
Notice that the pseudo tutor maththerapy tries to bring race and sexism into this issue.
I am neither racist nor sexist. I don't really care what that fool thinks of me. I am not convinced he can think!
I am sure that you have noticed that I have been praising your lessons and the time and effort you put into this website. I have nothing personal against you.
Let up on how you criticize other tutors. You know who I am mean.

Answer by ikleyn(52864) About Me  (Show Source):
You can put this solution on YOUR website!
.
It means that 


    a%2A%281%2F2%29%5E1 + b%2A%281%2F3%29%5E1 = 5%2F6      (1)    (at n= 1)

    a%2A%281%2F2%29%5E2 + b%2A%281%2F3%29%5E2 = 19%2F36     (2)    (at n= 2)

or

    a%2A%281%2F2%29 + b%2A%281%2F3%29 = 5%2F6       (1')  

    a%2A%281%2F4%29 + b%2A%281%2F9%29 = 19%2F36      (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%2A%281%2F4%29 + b%2A%281%2F6%29 = 5%2F12       (3)  

    a%2A%281%2F4%29 + b%2A%281%2F9%29 = 19%2F36       (4) 


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


                     b%2A%281%2F6-1%2F9%29 = 5%2F12-19%2F36,   or


                     b%2A%281%2F18%29 = -4%2F36 = -2%2F18

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.


If you still have questions, then let me know.