Can someone explain for me those three question below. I got those answer from w

Question

Can someone explain for me those three question below. I got those answer from wolframalpha, but can someone tell me why it do so?

I know the geometric series is a*r^n , and if ?r?< 1 then is is converge. but for the first one, the r should be 4 right ? why it is converge?

Did i miss something ? for me the first one is oo. but wolframalpha said is 6.

please help.

Can someone explain for me those three questions below. I got those answer from wolfram alpha, but can someone tell me why it do so? I know the geometric series is a*r^n , and if ?r?

Explanation / Answer

3. Factor the 4 out of the sum. The ratio is then seen to be 1/3, and thus it converges to

4 * [1/(1-1/3)] = 4 * 3/2 = 6

4. Again, factor the 2 out of the sum. The ratio is then -3/8, and the sum converges to

2 * [ 1/ (1 - (-3/8) ] = 2 * (8/11) = 16/11

5. If the 2 is factored out, then the ratio is seen to be 5/3, which is greater than 1. The series diverges.

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