Question

The sum 'S' of the first n natural numbers is S=n(n+1)/2. Find n if sum is 55​

Answer 1

$55 = \frac{n(n + 1)}{2} \\ 110 = {n}^{2} + n \\ {n}^{2} + n - 110 = 0 \\ {n}^{2} - 10n + 11n - 110 = 0 \\ n(n - 10) + 11(n - 10) = 0 \\ (n + 11)(n - 10) = 0$

Therefore, n = 10 (Neglect -11 because n is never -ve)

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Answer 2

Answer: n= 10

Step-by-step explanation:

n^2+n=55*2

n^2+n-110=0

n^2+11n-10n-110=0

n(n+11)-10(n+11)=0

(n+11)(n-10)=0

n=-11(not possible),

therefore n=10 Ans