Question

Please explain this method to solve series?

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!!

Answer 1

Please see the Explanation.

Explanation:

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