Please explain this method to solve series?

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Note:- I can do this question with another method but i want to know about this method. But I am not able to understand from E.Q-(1) so please explain this method & there is no need to solve question .
PLEASE EXPLAIN.
Thanks in advance!!

1 Answer
Aug 8, 2018

Please see the Explanation.

Explanation:

As per eqn.(1), (2r-3)t_r+8t_r=(2r-1)t_(r+1)(2r3)tr+8tr=(2r1)tr+1.

:. 8t_r=(2r-1)t_(r+1)-(2r-3)t_r

Now, we want to express t_r as f(r)-f(r+-1).

So, let us see if we succeed if we take f(r)=(2r-3)t_r.

f(r)=(2r-3)t_r rArr f(r+1)={2(r+1)-3}t_(r+1),

i.e., f(r)=(2r-3)t_r rArr f(r+1)=(2r-1)t_(r+1).

Thus, we have been successful to express t_r as,

f(r+1)-f(r)," with, "f(r)=(2r-3)t_r.