- #1
HallsofIvy said:The point is that both of your series are geometric series. What you do in your last post is essentially repeating the proof that the sum of the geometric series, [itex]\sum_{n=0}^\infty r^n[/itex] is [itex]\frac{1}{1- r}[/itex] except that you have [itex]r= \frac{1}{\gamma}[/itex].
Mentallic said:There is no mention of infinite sums.
musicgold, so what is
[tex]\sum_{i=1}^{n}\frac{1}{1+y}[/tex]
musicgold said:Please see the attached file.
I think, I am close, but not sure how to get rid of the 'y' in the encircled term.
What am I missing?
To simplify a summation formula, you can try breaking it down into smaller parts and using known mathematical operations such as addition, subtraction, and multiplication. You can also look for patterns in the formula and use known mathematical identities to simplify it.
If you are unable to simplify a summation formula, you can try using a calculator or computer program to evaluate the formula for specific values of the variables. You can also seek help from a math tutor or teacher who can provide guidance on solving the formula.
Yes, there are several general techniques for simplifying summation formulas. These include using known mathematical identities, breaking the formula into smaller parts, and using properties of summation such as linearity and distributivity.
Yes, algebraic manipulation is a common technique used to simplify summation formulas. You can use algebraic rules such as the distributive property, associative property, and commutative property to rearrange and simplify the terms in the formula.
No, not all summation formulas can be simplified. Some formulas may be inherently complex and cannot be simplified using known mathematical techniques. In these cases, it is best to use a calculator or computer program to evaluate the formula for specific values.