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

Course Queries Syllabus Queries 3 years ago

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manpreet Tuteehub forum best answer Best Answer 3 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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