The best way to solve this..
1+ 3+6 +10+....Tn=8436
> 1+ (1+2)+ (1+2+3)+(1+2+3+4)+....+(1+2+3+..+n)=8436
in terms of n
ΣΣ n=8436
>> Σ n(n+1)/2=8436
>> Σ n^2 +Σ n=16872
now since n^2 increases in higher rate that n..in this equation Σn^2 would be contributing factor..So lets concentrate on Σn^2 part only
now Σn^2= n(n+1)(2n+1)/6 =16872
looking at the answer option lets try with middle value 40..
Above equation would be in approx
40*40*80/6=21K (in approx) so Answer must be less than 40
now lets try with n=30
30*30*60/6=9000(a way below of 16872) .so answer must be above 30
hence answer must be 36
36*37*73/6= 16206 (nearest value of 16872)
1+ 3+6 +10+....Tn=8436
> 1+ (1+2)+ (1+2+3)+(1+2+3+4)+....+(1+2+3+..+n)=8436
in terms of n
ΣΣ n=8436
>> Σ n(n+1)/2=8436
>> Σ n^2 +Σ n=16872
now since n^2 increases in higher rate that n..in this equation Σn^2 would be contributing factor..So lets concentrate on Σn^2 part only
now Σn^2= n(n+1)(2n+1)/6 =16872
looking at the answer option lets try with middle value 40..
Above equation would be in approx
40*40*80/6=21K (in approx) so Answer must be less than 40
now lets try with n=30
30*30*60/6=9000(a way below of 16872) .so answer must be above 30
hence answer must be 36
36*37*73/6= 16206 (nearest value of 16872)
