needingtoknow said:Homework Statement
How to get from
Sum of 2(cos((3pi)/(2^(k+1)))sin(pi/(2^(k+1)))) from k = 1 to infinity
to
Sum of sin((4pi)/(2^(k+1))) - sin((2pi)/(2^(k+1))) from k = 1 to infinity
The two expressions are equivalent. I need help getting from the first expression to the second.
The purpose of rewriting a sum in another form is to simplify or manipulate the expression in order to better understand or solve the problem at hand. It can also help to identify patterns or relationships between the terms in the sum.
The form that you choose to rewrite the sum in depends on the specific problem and what you are trying to achieve. Some common forms include factoring, expanding, and simplifying using algebraic properties.
Yes, it is often helpful to rewrite a sum in multiple forms in order to fully understand and solve the problem. However, it is important to make sure that the different forms are equivalent to ensure accuracy in your solution.
There is no one specific method for rewriting a sum in another form, as it will vary depending on the problem. However, it is helpful to follow the order of operations and use algebraic rules and principles to guide your process.
Some tips for effectively rewriting a sum in another form include identifying and factoring out common factors, using the distributive property, and simplifying by combining like terms. It is also important to check your work and make sure all forms are equivalent.