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How do you solve for n in #S = (n(n+1))/ 2#?

Answer 1

Hazel Anglin

# n = (-1 +- sqrt(1+8S))/(2) #

# S = (n(n+1))/2 #

# S = (n^2+n)/2 #

# 2S = n^2 +n #

# n^2 + n - 2S = 0#

using the quadratic formula for : # ax^2 + bx + c = 0#,

# n = (-b +- sqrt( b^2 - 4ac) ) /(2a) #

# n = (-1 +- sqrt(1 - 4(1)(-2S)))/2 #

# n = (-1 +- sqrt(1+8S))/(2) #

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Answer 2

Eva Adamson

To solve for ( n ) in the equation ( S = \frac{n(n+1)}{2} ), you can rearrange the equation to isolate ( n ) and then solve for it. Here's the step-by-step process:

Multiply both sides of the equation by 2 to eliminate the fraction: ( 2S = n(n+1) ).
Expand the expression on the right side: ( 2S = n^2 + n ).
Rearrange the equation into a quadratic form: ( n^2 + n - 2S = 0 ).
Use the quadratic formula to solve for ( n ): ( n = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ), where ( a = 1 ), ( b = 1 ), and ( c = -2S ).
Substitute the values of ( a ), ( b ), and ( c ) into the quadratic formula and solve for ( n ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.