What are the solutions to the equation (n(n+1))/2 =5050 ?

The solutions to the equation (n(n+1))/2 =5050 are n=100,n=-101

Find the zeros of (n(n+1))/2 =5050

The zeros of (n(n+1))/2 =5050 are n=100,n=-101

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\frac{n ( n + 1 )}{2} = 5050

n = 100, n = - 101

Solution steps

\frac{n ( n + 1 )}{2} = 5050

Multiply both sides by

2

n (n + 1) = 10100

Expand

n (n + 1) : n^{2} + n

n^{2} + n = 10100

Move

10100

to the left side

n^{2} + n - 10100 = 0

Solve with the quadratic formula

n_{1, 2} = \frac{- 1 \pm 1 ^{2} - 4 \cdot 1 \cdot ( - 10100 )}{2 \cdot 1}

1^{2} - 4 \cdot 1 \cdot (- 10100) = 201

n_{1, 2} = \frac{- 1 \pm 201}{2 \cdot 1}

Separate the solutions

n_{1} = \frac{- 1 + 201}{2 \cdot 1}, n_{2} = \frac{- 1 - 201}{2 \cdot 1}

n = \frac{- 1 + 201}{2 \cdot 1} : 100

n = \frac{- 1 - 201}{2 \cdot 1} : - 101

The solutions to the quadratic equation are:

n = 100, n = - 101

x, 3 x^{2} - 3 y = 3 y^{2} - 3 x

x^{2} + 1 = 48

x^{2} + 4 x - 42 = 3

x^{2} - 14 = - 10

- x^{2} + 169 x - 28 = 0

What are the solutions to the equation (n(n+1))/2 =5050 ?
The solutions to the equation (n(n+1))/2 =5050 are n=100,n=-101
Find the zeros of (n(n+1))/2 =5050
The zeros of (n(n+1))/2 =5050 are n=100,n=-101