Tuesday, 19 November 2019

sequences and series - find the sum to n term of frac11cdot2cdot3+frac32cdot3cdot4+frac53cdot4cdot5+frac74cdot5cdot6+...



1123+3234+5345+7456+...



=nk=12k1k(k+1)(k+2) =nk=112k+nk=13k+1nk=152(k+2)



I do not know how to get a telescoping series from here to cancel terms.


Answer



HINT:




Note that we have



2k1k(k+1)(k+2)=3k+15/2k+21/2k=12(1k+11k)+52(1k+11k+2)


No comments:

Post a Comment

real analysis - How to find limhrightarrow0fracsin(ha)h

How to find lim without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...