Question

Express the series using sigma notation. 2 - 6 + 18 – 54 + 162 ...

Answer 1

The given series can be expressed using sigma notation as ∑ (2 * (-3)^(n-1)).

Step-by-step explanation:

The given series can be expressed using sigma notation as:

∑ (2 * (-3)^(n-1)), where n ranges from 1 to ∞.

This formula represents the pattern in the series where each term is obtained by multiplying the previous term by -3. The exponent in each term increases by 1.

Answer 2

`2-6+18-54+162+\cdots=2(-3)^0+2(-3)^1+2(-3)^2+2(-3)^3+2(-3)^4+\cdots`

`=\displaystyle2\sum_(n=0)^\infty(-3)^n`