Question

how do I write this is sigma notation? infinite geometric series where a1 = 42 and the common ratio is three fourths.

Answer 1

\[\Large 42\sum_{n = 1}^{\infty}(\frac 34)^{n-1}\]

Answer 2

well its almost right try

\[\sum_{n = 1}^{\infty} 42 \times (\frac{3}{4})^{n - 1}\]

n = 1 you get the 1st term 42

Answer 3

one more thing it's divergent right? because its infinite

Answer 4

its convergent because the common ratio is between -1 < r < 1

when that occurs you have a convergent sequence