75 points for the best ! , show all your work. does this series converge or diverge? and if it converges what is the sum? ∞ ∑ -4(-1/2)^n-1 n=1

Answers: the sum is convergentthe sum is -8/3======i assume this is what it looks like    for a geometric series, when  the common ratio r satisfies  |r| < 1, the series is convergent. the geometric series converges because the absolute value of the common ratio (|-1/2| = 1/2) is less than 1.the sum for an infinite geometric series is given by    s = a / (1 - r)where a is the first term and r is the common ratio.the first term is -4 since when we use the lower bound of summation (n=1) into the summand  -4(-1/2)^(n-1), we get -4 as the first term.the sum is    s = -4 / ( 1 - (-1/2) ) = -4/( 2/2+1/2 ) = -8/3    the sum is -8/3.