Question

\sum _{n=1}^{\infty }−4\left(\frac{−1}{2}\right)^{n-1}

Answer 1

Answer:
`\bold{-(8)/(3)}`

Explanation:

`\sum \limits_(n=1)^(\infty)-4\bigg((-1)/(2)\bigg)^(n-1)\implies a_1=-4, r=-(1)/(2)\\\\\\\text{Use the formula for the sum of an infinite geometric series:}\\S=(a_1)/(1-r)\\\\\\.\ =(-4)/(1-(-(1)/(2)))\\\\\\.\ =(-4)/((3)/(2))\\\\\\.\ =-4* (2)/(3)\\\\\\.\ =\large\boxed{-(8)/(3)}`