Math: Convergent or Divergent?

ted s2021-03-31T18:45:53Z

Favorite Answer

it is actually " absolutely convergent ".....8 ( 1 / [ 1 + 7/8 ] )

stanschim2021-03-31T18:03:33Z

The series diverges.

Writing out each term and applying the factor, 8, to each gives:

1 - 7 + 7^2 - 7^3 + 7^4 - 7^5 +...+ (-7)^k

This is clearly a geometric series with a ratio of -7.  Since the absolute value of the ratio is not less than 1, the series must diverge.