Consider the infinite series defined by

(a)

(b)

if r<1, then it converges absolutely

if r>1, then it diverges

if r=1, then the test is inconclusive

Step-by-step explanation:

The ratio test is:

if L<1, then it converges absolutely

if L>1, then it diverges

if L=1, then the test is inconclusive

I'm assuming that they used r instead of L. Anyway, to do the ratio test, you plug in n+1 into the equation and make that numerator.

Then you plug in n into the same equation and make that your denominator.

In our case, our equation is .

So lets plug in n+1 and make that our numerator.

Now lets plug in n and make that our denominator.

Now set up the ratio test.

if you simplify this, you would get (view image for the steps)

L = infinity, which is > 1, therefore this series diverges

i believe it is d.) buddhism and e.) hinduism

1/2(2*4)=6 $$- agahajakanajak