Saved Bookmarks
| 1. |
`lim_(n->oo) (1^p+2^p+3^p+...........+n^p)/n^(p+1)`A. `1/(p+1)`B. `1/(1-p)`C. ` 1/p - 1/(p-1)`D. `1/(p+2)` |
|
Answer» Correct Answer - A Given , `lim_(ntoinfty)(1^(p)+2^(p)+3^(p)+...+n^(p))/(n^(p+1))=lim_(ntoinfty)sum_(r=1)^(n)[(r^(p))/(n^(p+1))]` `=lim_(ntoinfty)(1)/(n)sum_(r=1)^(n)((r)/(n))^(p)=int_(0)^(1)x^(p)dx=[(x^(p+1))/(p+1)]_(0)^(1)=(1)/(p+1)` |
|