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Hey guys, I am attempting to prove a question that I found from a problem set from Stanford Uni on series and sequences, however I'm having a little bit of difficulty. I've been at it for a while and so finally i've resorted to looking at the provided solution. The question and solution are...

By using the graph of y = cos x for 0 ≤ x ≤ 2π, or otherwise, find those values of x satisfying the given domain for which the geometrical series 1 + 2 cos x + 4 cos2x + 8 cos3x + ... has a limiting sum. I was wondering if anybody could please provide me a solution by using the 'or otherwise'...

Here's an upload of a bank of multiple choice questions covering all 8 topics for anyone who wants to get some more exposure to multiple choice style questions. There's over a 100 questions and I've also uploaded the worked solutions. If anyone notices any mistakes in the solutions just tell me...

Hey can someone please help me with this proof that I'm having trouble with, any help is appreciated

School rank ~310 MXT2 - 1/4 MXT1 - 1/6 English Ad - 6/22 Legal Studies - 2/18 Business Studies - 3/7 (Probably won't count for ATAR by the looks of things) Physics - 1/9 Atar aim is 95 Thank you :)

Hey guys just having some trouble with this question, any help is appreciated.

I need some help gathering some information on what the impacts of transformers would be on society(disadvantages only) and the impact of transformers on the environment(advantages and disadvantages)? Any ideas? Thanks

Hey can someone please explain to me how to do this vector question from the Arnold textbook. Sorry I don't know how to use Latex yet. Show that ||z1| - |z2|| ≤ |z1 + z2|. State the condition for the equality to hold. Thanks