Proof of ∑ki=1(2i−1)=k2 and some general questions

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Posted on 16 Aug 2022, this text provides information on Syllabus Queries related to Course Queries. Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.

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manpreet Tuteehub forum best answer Best Answer 2 years ago

 

My vocabulary in math is lacking quite a lot, so please forgive me if my question is not sufficiently accurate or needlessly verbose. I tried very hard to get the latex flowing, at least that's one thing I got going.

In the syllabus from which I'm currently studying, the proof of this equation is something I have difficulty grasping (this is a quick example that's supposed to be self-explanatory *desperate face*):

 

i=1k(2i1)=k2∑i=1k(2i−1)=k2

 

Now, this is the proof in the syllabus:

 

i=1k+1(2i1)=i=1k(2i1)+2k+1∑i=1k+1(2i−1)=∑i=1k(2i−1)+2k+1

 

 

i=1k+1(2i1)=k2+2k+1∑i=1k+1(2i−1)=k2+2k+1

 

 

i=1k+1(2i1)
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