sum of series question

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Sonal7

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I cant work out how they have cancelled the terms to get an expression for the sum of the series. I Screenshot 2020-05-29 at 21.01.53.png

Now I cant see how the 2/3 comes from and I can sort of see that where -2/(n-2) and 1/(n-1) have come from but what happened to the -1/(n-3) in the last two lines above. I can see that -3/(n-3) and 2/(n-3) will give you -1/(n-3).
Screenshot 2020-05-29 at 21.02.01.png
 
Combine the first term in each parenthesis (top right of your post, last equation). Then combine the 2nd term from each parenthesis and then do the same with the 3rd. Now do you see cancelling out or combining? Try it!

You might also try to see if you see a pattern of the value in each parenthesis.
 
I cant see it. I am getting 37/60, -47/20 and 13/6 when i add the first terms, 2nd terms and 3rd terms in the first, second and third parenthesis. I cant see any pattern! oh no, i can see a pattern, finally give me minute.
 
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no not much luck the last two terms in the first bracket cancel. -3/3 and 2/2. and the 1/4 and -3/4 and 2/4 cancel out. It all looks messy
 
I have an idea. i will practise some simpler examples and see if it works by tonight!
 
You did not understand me so I will try again. There are many many parenthesis ( ). In each one there are three terms. Take the 1st term from the 1st parenthesis, the first term from the 2nd set of parenthesis, the first term from the 3rd set of parenthesis all the way to the last set of parenthesis where you take the first term. Combine all those term into one parenthesis.

Then do the same for all the 2nd terms and then finally for all the 3rd terms. Combine all these set of parenthesis and try to see a pattern.
 
but you dont know all the terms so how many from the first few and how many for the very last few. It seems hard. I shall look at this in the morning as the brain works better then.
 
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Sonal7 said:
but you dont know all the terms so how many from the first few and how many for the very last few. It seems hard. I shall look at this in the morning as the brain works better then.
Click to expand...
The last sum in parentheses shows you what the last terms are.
 
Sonal7 said:
but you dont know all the terms so how many from the first few and how many for the very last few. It seems hard. I shall look at this in the morning as the brain works better then.
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That is just why the final answer is in terms of n. For example, 1+ 2 + 3 + ... + n = n(n+1)/2. The sum is in terms of n
 
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i know what n! means please dont dumb it down. I am still working on this.
 
Sonal7 said:
I cant see the pattern at all :(
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Write out a few more terms. You'll see fractions with equal denominators and different signs - good candidates for cancelling. E.g. 1/4, -3/4, 2/4, etc.
 
lev888 said:
Write out a few more terms. You'll see fractions with equal denominators and different signs - good candidates for cancelling. E.g. 1/4, -3/4, 2/4, etc.
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so not saying Jomo is not accurate. This complete contradicts what you asked me to do earlier adding middle terms, and end terms etc just wont work! completely different denominators. I guess you need to cancel the first from the 2nd and then the last etc.
 
I can see that in the first term -3/3 and 2/2 cancel but that leaves 1/4. -3/4 and 2/4 gives -1/4 so that cancels.
 
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