These do start with 41 and 41^2 instead of 1 and 1^2, but the formula they have (the ##\frac{x(x+1)}{2}##) is for the sequence that starts with 1.
So that means that you can rewrite the formula given as a sigma notation from 1 to n and then simplify from there.
Homework Statement
If r is a rational function, use Exercise 57 to show that ##\mathop {\lim }\limits_{x \to a} \space r(x) = r(a)## for every number a in the domain of r.
Exercise 57 in this book is: if p is a polynomial, show that ##\mathop {\lim }\limits_{x \to a} \space p(x) = p(a)##...
That is true if it is just the quadratic equation, but if you are dividing two numbers what happens if they are each positive? Each negative? One positive and one negative?
You need to use the answers to those questions to determine the sign of the division of two functions.
I don't know if you want a mathematical method for doing a problem like this, but I would approach it by saying that if a person speaks only English, than they don't speak Spanish or Swahili.
So there are 100 people, and at least 60 of them don't fit in the set of people who only speak English...
It does effect the acceleration of the mass system because as the mass drops, energy is transferred into the pulley as well, instead of remaining in the system.
Ah okay :)
You said that you get the correct answer when you use the formula with a ##2g## in the denominator instead of just ##g##, and when you use the ##g## formula you get it wrong.
But when you use the formula with just a ##g##, did you recalculate your ##V_o##?