How many terms of the series “1 + 2 + 3 ......” add

Let the number of terms be n.
∴ 1 + 2 + 3 + ..... + n = 5050

⇒	n (n + 1)	= 5050
	2

⇒ n (n + 1) = 10100
[or use splitting middle term method]
⇒ n (n + 1) = 100 × 101
⇒ n (n + 1) = 100 (100 + 1)
⇒ n = 100