can someone explain to me how they get this :
∑_(r=1)^n▒u_r = ∑_(r=1)^n▒r(r+1)

= r(r+1)(r+2) - (r-1)r(r+1)

by using the method of difference , I stil don't get it why they end up like that,,,

Question

can someone explain to me how they get this :
 ∑_(r=1)^n▒u_r = ∑_(r=1)^n▒r(r+1) 

= r(r+1)(r+2) - (r-1)r(r+1) 

by using the method of difference , I stil don't get it why they end up like that,,,

cruffo · Answer

I'm not seeing the problem correctly, looks like some things are missing. could someone type this out .

cruffo · Answer

$$\large \sum_{r=1}^n ? u_r = \sum_{r=1}^n ?r(r+1) = (r+1)(r+2) - (r-1)r(r+1)$$

anonymous · Answer

i want to ask my own questions

anonymous · Answer

this problem same as this question : 

Find the sum of  n  terms of the series 1.4.7 + 4.7.10 + 7.10.13

$$U_{r}$$ = (3r-2)(3r+1)(3r+4)

Form another sequence  Vr  by adding one more factor to the end of the general term  Ur  

$$V_{r}$$ = (3r-2)(3r+1)(3r+4)(3r+7)
$$V_{r-1}$$ = (3r-5)(3r-2)(3r+1)(3r+4)

my question is : how they get the another factor in the general term & add it to another sequence ? In this case for $$V_{r}$$ they get the another factor is (3r+7) and for $$V_{r-1}$$ they get (3r-5)...HOW...????