i'm trying to do some calc hw, but i ran into this equation
∞
Σ t^k = 5
k=0
is there some kind of rule which changes this equation so i can solve for k?
Solve for k?!? That makes no sense you probably mean for tOriginally Posted by hongster5
This is,
Assuming that this infinite series converges then it is a geometric series for and such as its sum is 5. But its sum is given by .
Thus,
thus,
Q.E.D.
Something interesting to note,
the eqaution
Always has a unique solution,
namely,
and that,
Thus, any infinite geometric sum can be made to converge to any real number.