Answer:
220
Step-by-step explanation:
we want to figure out Sum of the following series:
[tex] \rm(1) + (1+2) + (1+2+3) + { \dots}+ (1+2+3+{\dots}+10)[/tex]
notice that, the nth term is equal to the sum of all the previous and the nth term , therefore the nth term of the sequence is 10 . The sum of the sequence is equal to
[tex] \displaystyle S _{n} = \frac{n(n + 1)(n + 2)}{6} [/tex]
see the following question for more information
since we've already figured out n=10 therefore substitute:
[tex] \displaystyle S _{10} = \frac{10(10+ 1)(10+ 2)}{6} [/tex]
simplify parentheses:
[tex] \displaystyle S _{10} = \frac{10(11)(12)}{6} [/tex]
simplify multiplication:
[tex] \displaystyle S _{10} = \frac{1320}{6} [/tex]
simplify division:
[tex] \displaystyle S _{10} = \boxed{220}[/tex]
hence, the Sum of the series is 220
