Let the positive integers be written in the form : If the k^ th row contains exactly k numbers for every natural number k , then the row in which the number 5310 will be, is _______

Step-by-step solution

aligned & S =1+2+4+7+ + T _ n & S =1+2+4+ & Tn =1+1+2+3+ + ( T _ n - T _ n -1 ) & T _ n =1+ ( n -1 2 )[2+( n -2) 1] & T _ n =1+1+ n ( n -1) 2 & n =100 ~T _ n =1+ 100 99 2 =4950+1 & n =101 ~T _ n =1+ 101 100 2 =5050+1=5051 & n =102 ~T _ n =1+ 102 101 2 =5151+1=5152 & n =103 ~T _ n =1+ 103 102 2 =5254 & n =104 ~T _ n =1+ 104 103 2 =5357 aligned