Question

Find the sum of the given series:(1) + (1+2) + (1+2+3) + ... + (1+2+3+...+10)​

Answer 1

Answer:

220

Step-by-step explanation:

we want to figure out Sum of the following series:

$\rm(1) + (1+2) + (1+2+3) + { \dots}+ (1+2+3+{\dots}+10)$

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

$\displaystyle S _{n} = \frac{n(n + 1)(n + 2)}{6}$

see the following question for more information

• brainly.com/question/24416228

since we've already figured out n=10 therefore substitute:

$\displaystyle S _{10} = \frac{10(10+ 1)(10+ 2)}{6}$

simplify parentheses:

$\displaystyle S _{10} = \frac{10(11)(12)}{6}$

simplify multiplication:

$\displaystyle S _{10} = \frac{1320}{6}$

simplify division:

$\displaystyle S _{10} = \boxed{220}$

hence, the Sum of the series is 220