Solve

RPF..you are a real genius yaar..[12]

Mast hai yaar!

Goodness me,you are indeed a genius.

A small help though, how did you derive this
'2n^2+n+6'

Just by inspection ? or is there any shortcut for that ?

I guess inspection...coz thats how I reached there too..

there is a theory to determine the degree of T_n

the method

let

T1 T2 T3 T4 T5 ......... be terms of seq

let

S1 S2 S3 S4 ........be T2-T1 ,T3-T2,.........respectively

if S1 S2 S3 .are in AP

then

Tn is quadratic in n

so put

Tn=an^2+bn+c
plug the first three terms to solve a , b,and c

if S1,S2,S3..are not in AP

then again take differnce and if that is in AP
Tn is cubic in n

likewise procced and increase the dgree each time [1]

the proof is not tuff

(x)^n-(x-a)^n will be of degree x^(n-1)

now u will realise i am not a genius , damn me , why did i tell this method

How crude my inspection method looks in front of this...:(

dont think like that guruji... u got the q thats god

methods become good as time passes and as u solve more and more q