which expression represents the second partial sum for ∑_{n = 1}^∞ 3(1/2)^{n - 1}?\n3(1/2)^0+3(1/2)^1\n3(1/2)…

which expression represents the second partial sum for ∑_{n = 1}^∞ 3(1/2)^{n - 1}?\n3(1/2)^0+3(1/2)^1\n3(1/2)^1+3(1/2)^2\n1/2(3)^0+1/2(3)^1\n1/2(3)^1+1/2(3)^2

which expression represents the second partial sum for ∑_{n = 1}^∞ 3(1/2)^{n - 1}?\n3(1/2)^0+3(1/2)^1\n3(1/2)^1+3(1/2)^2\n1/2(3)^0+1/2(3)^1\n1/2(3)^1+1/2(3)^2

Answer

Explanation:

Step1: Recall partial - sum formula

The $k$-th partial sum of a series $\sum_{n = 1}^{\infty}a_{n}$ is $S_{k}=\sum_{n = 1}^{k}a_{n}$. For the series $\sum_{n = 1}^{\infty}3(\frac{1}{2})^{n - 1}$, when $k = 2$, we need to find $S_{2}=a_{1}+a_{2}$.

Step2: Find $a_{1}$ and $a_{2}$

When $n = 1$, $a_{1}=3(\frac{1}{2})^{1 - 1}=3(\frac{1}{2})^{0}=3\times1 = 3$. When $n = 2$, $a_{2}=3(\frac{1}{2})^{2 - 1}=3\times\frac{1}{2}$. So $S_{2}=3(\frac{1}{2})^{0}+3(\frac{1}{2})^{1}$.

Answer:

$3(\frac{1}{2})^{0}+3(\frac{1}{2})^{1}$