Question

In the following exercises Write the series using summation notation ?

4+7+12+19+...

-3+4-5+6-7

1/3+1/9+1/27+1/81+....

Answer 1

`4+7+12+19...=sum_(k=1)^nk^2+3`

`-3+4-5+6-7...=sum_(k=1)^(n)(-1)^k(k+2)`

`1/3+1/9+1/27+1/81...=sum_(k=1)^n1/(3^k)`

where `n` = the number of terms in the series.

Explanation:

Normally, I don't do people's homework for them, but since you're new to Socratic, I'll do yours. Welcome.

`4+7+12+19...=sum_(k=1)^nk^2+3`

`-3+4-5+6-7...=sum_(k=1)^(n)(-1)^k(k+2)`

`1/3+1/9+1/27+1/81...=sum_(k=1)^n1/(3^k)`

where `n` = the number of terms in the series.