If $f_1, f_2, f_3,\ldots$ is the Fibonacci sequence proof $f_1^2 + f_2^ 2 + \cdots + f_n^2 = f_n f_{n+1}$.
For the Fibonacci numbers, show for all $n$: $F_1^2+F_2^2+\dots+F_n^2=F_nF_{n+1}$
So if I'm correct, when you chose your starter gear and wealth you can either choose to roll some dice depending on your class and buy everything from that or you can choose the starter gear from your class and add the background items (including some gold). Here are my 2 questions:   If I choose the gear from my class, do I have to take all the equipment from only one of the (a) or (b) choices, or can I freely mix-and-match choices from the two sets? Can you spend the extra gold you get from your background on extra equipment (e.g. some soap and some fishing equipment) or do you have to start with that gold in its pouch?   The reason I ask is that I have recently created a level 1 wood elf druid and I mixed-and-matched the gear from the class, so that I chose a shortbow as a "(b) simple weapon" for the first point and a "(a) Scimitar" at the second point. My DM wasn't so happy about this, as he can't understand why I'm mixing (a) and (b).  He also wasn't so happy with me spending my 10gp from my outlander background. I decided that my druid wouldn't lay so much worth in 10gp compared to a bunch of stuff I got for that (e.g. some soap and some fishing equipment and some other useful things) and he seems to think that I'm supposed to just start with the gold instead. This is a question of the book Linear Algebra of Kenneth Hoffman.  Describe explicitly all inner products on $\mathbb{R}$ and on $\mathbb{C}$.  I think that if $&lt;,&gt;$ is one inner product on $\mathbb{R}$ (or $\mathbb{C}$) then $&lt; ,&gt;=K[,]$, where $[,]$ is the standard inner product. Is that correct? As far as I can tell downvoting is mostly useless.     For questions the only people who get downvoted are lower rep users, or incredibly stupid questions    most questions that are downvoted get closed anyway which should be sufficient downvoting doesn't have too much affect on your rep anyway a negative comment is more useful and more of a push too change or delete the question  For answers downvoting is often used incorrectly as well   people commonly competitively downvote (downvoting another answer to a question that you also answered) obviously not a good behavior downvoting (and upvoting) are contagious, meaning one downvote leads to a bunch of others even though downvotes don't effect rep that much they create a negative environment, no one wants their post downvoted, on the other hand criticizing comments, I think, are far more welcome      So basically in a nutshell a downvote serves no real purpose even if a post deserves it. Flagging, closing and commenting are much more useful to everyone including the poster than downvoting so why have it.    I now see from the answers and comments that downvotes do serve a purpose and would like to retract my request. Entire function bounded by a polynomial is a polynomial Suppose that an entire function $f(z)$ satisfies $\left|f(z)\right|\leq k\left|z\right|^n$ for sufficiently large $\left|z\right|$, where $n\in\mathbb{Z^+}$ and $k&gt;0$ is constant. Show that $f$ is a polynomial of degree at most $n$. How do I fix these M4 macro errors? I am trying to compile  but when I run ./autogen.sh the script terminates with these errors  Checking for required M4 macros...   libtool.m4 not found   glib-gettext.m4 not found   intltool.m4 not found   pkg.m4 not found   gtk-doc.m4 not found   yelp.m4 not found ***Error***: some autoconf macros required to build mate-desktop   were not found in your aclocal path, or some forbidden   macros were found.  Perhaps you need to adjust your   ACLOCAL_FLAGS?   What do I need to do to get rid of these errors? I tired installing the latest versions of inittool, glib, gtk, yelp, etc... but I still get the macros errors. Can you explain the "Axiom of choice" in simple terms? As I'm sure many of you do, I read the  webcomic regularly. The  involves a joke about the Axiom of Choice, which I didn't get.     I went to Wikipedia to see what the Axiom of Choice is, but as often happens with things like this, the Wikipedia entry is not in plain, simple, understandable language. Can someone give me a nice simple explanation of what this axiom is, and perhaps explain the XKCD joke as well? Word for sentences that make sense when read backwards? Is there a word for sentences that make sense when read normally or backwards (not necessarily by reversing the words)? Example:     "Are you as bored as I am?" Identify an unknown IP in our network I have a network containing 20 clients. I assigned IP range 10.0.0.1 to 10.0.0.20 to them. When I do an IP scanning I see someone using 10.0.0.131 in VMware. How can I find out which IP is this IP bridged with? i.e How can I find out which system has 2 IP? (i.e the other IP of this system)  Update:  My system IP in the network is 10.0.0.81:    Output of the IP scanner show someone using 10.0.0.131 in VMware:    And the result of tracert command show nothing between us:  C:\Users&gt;tracert -j 10.0.0.131 10.0.0.81  Tracing route to ghasemi3.it.com [10.0.0.81] over a maximum of 30 hops:    1    &lt;1 ms    &lt;1 ms    &lt;1 ms  ghasemi3.it.com [10.0.0.81]  Trace complete. C:\Users&gt; How many ways can $133$ be written as sum of only $1s$ and $2s$ Since last week I have been working on a way, how to sum $1$ and $2$ to have $133$.  So for instance we can have $133$ $1s$ or $61$ $s$2 and one and so on. Looking back to the example: if we sum: $1 + 1... + 1 = 133$ there is only one way. But for the second one there will be $131$ possible ways. And I have to do this for every possible combination. I am stuck with it and I have no idea whatsoever on how to begin.  Any ideas or methods I could use guys? Union of the conjugates of a proper subgroup Let G be a finite group and H be a proper subgroup. Prove that the union of the conjugates of H is not the whole of G.  Thanks for any help Convert integer to hexadecimal and back again Why define an anonymous function and pass it jQuery as the argument? Why are the dineutron and diproton unbound? Creating polygons as % of original area using ArcGIS Desktop? I have a polygon shapefile and need to create new polygons, within the originals, as % of original area.  I used buffer by field (Field= new area as %) but the buffers are created in circles around the polygons.  What am I doing wrong?  I am using ArcGIS Desktop 10. Why am I seeing two JPG files instead of RAW + JPG with a Canon 1100D? What is the correct position of the word 'also'?     I would like to also talk about ...      I would also like to talk about ... What happens when you put a Portable Hole inside a Bag of Holding while on the Astral plane? What would happen if someone were to place a Portable Hole within a Bag of Holding while being within the Astral Plane? Would it be the reverse effect? Using different delimiters in sed commands and range addresses Why are the holodecks on Voyager in use if they have energy issues? I'm watching the first two seasons of Voyager and various episodes have commentary on having energy limitations -- but we constantly see crew using extremely complicated holodeck simulations. Why would they allow use of the holodeck if they need to conserve energy? C# Compiler should give warning but doesn't?