Question

Sigma notation help?

Answer 1

`\sum\limits_(n=1)^6\big[4(-5)^(n-1)\big]`

is a sum of the first six terms of a geometric series where first term:


`a_1=4\cdot(-5)^(1-1)=4\cdot(-5)^0=4\cdot1=\boxed{4}`

and common ratio
`r = -5`. So the sum is:


`S_n=(a_1(1-r^n))/(1-r)\\\\\\\\ S_6=(4(1-(-5)^6))/(1-(-5))=(4(1-15625))/(6)=(2\cdot(-15624))/(3)=(-31248)/(3)=\\\\\\=\boxed{-10416}`