CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

Sum the following series to n terms $$1.4.7+4.7.10+7.10.13+....$$.


Solution

General term$$=\left( 3n-2 \right) \left( 3n+1 \right) \left( 3n+4 \right) $$
$$=27{ n }^{ 3 }+27{ n }^{ 2 }-18n-8$$
Sum to $${ n }^{ th }$$ term $$=27\sum { { n }^{ 3 } } +27\sum { { n }^{ 2 } } +18\sum { n } -8$$
$$=27\cfrac { { n }^{ 2 }{ \left( n+1 \right)  }^{ 2 } }{ 4 } +27\cfrac { \left( n \right) \left( 2n+1 \right) \left( n+1 \right)  }{ 6 } -18\cfrac { \left( n \right) \left( n+1 \right)  }{ 2 } -8$$
$$=n\left( n+1 \right) \left[ \cfrac { 27\left( { n }^{ 2 }+n \right)  }{ 4 } +\cfrac { 27\left( 2n+1 \right)  }{ 6 } -17 \right] $$

Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image