Question

Determine divergence or convergence of the series.

∑(n = 1, ∞) 20/(n^(3/4))

Answer 1

The best way will be to determine the ration of (n+1)th term to nth term.

Answer 2

If it is greater than 1 then the series will diverge and if it is less than 1 then the series will converge.

Answer 3

20/(1^3/4) great so this diverges?

Answer 4

See:

(n+1)th term = \(\cfrac{20}{(n+1)^\cfrac{3}{4}}\)

nth term = \(\cfrac{20}{(n)^\cfrac{3}{4}}\)

Now ratio = \(\cfrac{\cfrac{20}{(n+1)^\cfrac{3}{4}}}{\cfrac{20}{(n)^\cfrac{3}{4}}}\)

= ?

Answer 5

Thanks for breaking it down!!

Answer 6

No problem.

Enjoy your time at OS and best of luck for future.
Keep Practicing
Gud day