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# FP1 Standard result for r

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1. What's the difference between the result

and the result

2. (Original post by huiop)
What's the difference between the result

and the result

The first one is while the first one .
3. (Original post by B_9710)
The first one is while the first one where there are n b's.
so how would i know which one to use in a question which says

show that

so far i got to this

then i went to this

so that 4n is wrong so how would i know to use standard result for r instead of b?
4. (Original post by huiop)
so how would i know which one to use in a question which says

show that

so far i got to this

then i went to this

so that 4n is wrong so how would i know to use standard result for r instead of b?
Where does the come from?

5. (Original post by RDKGames)
Where does the come from?

whoops typing error i thought i could use x as a substitute for \times
6. (Original post by huiop)
whoops typing error i thought i could use x as a substitute for \times
As for the difference between and ;

If it's r, then you are adding 1+2+3+4+5+...+n because you are summing up the integers from r=1 up to r=n.

If it's a constant (like b), then you are adding b+b+b+b+b+...+n because you are summing up a constant b, in a series of b, b, b, b, b, b, .... where every single term is b. So r=1 will be b, and r=2 will be b, and r=3 and so on up to r=n. Hence where nb comes from. As you are summing b an n amount of times.
7. (Original post by RDKGames)
As for the difference between and ;

If it's r, then you are adding 1+2+3+4+5+...+n because you are summing up the integers from r=1 up to r=n.

If it's a constant (like b), then you are adding b+b+b+b+b+...+n because you are summing up a constant b, in a series of b, b, b, b, b, b, .... where every single term is b. So r=1 will be be, and r=2 will be b, and r=3 and so on up to r=n. Hence where nb comes from. As you are summing b an n amount of times.
ok thanks for clarification
8. (Original post by huiop)
so how would i know which one to use in a question which says

show that

so far i got to this

then i went to this

so that 4n is wrong so how would i know to use standard result for r instead of b?
Think about what this notation means. If you have since there are n 1's. Using this notation, the sum is with respect to only. So if we have not .

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