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Determine if the following series is convergent or divergent by using Radio Test.
Solution
With this first illustration let's be a little careful and ensure that we have everything down correctly. Now Here are the series terms an.
an = (-10)n/42n+1 (n+1)
Remind that to compute an+1 all that there is a requirement to do is substitute n+1 for all the n's in an.
an+1 = (-10)n+1/ 42(n+1)+1 ((n+1)+1
= (-10)n+1/ 42n+3 (n+2)
Now, to illustrate L we will use,
As this will be a little easier while dealing with fractions like we've got here. Thus,
Thus, L<1 and so by the Ratio Test the series converges absolutely and therefore will converge.
Evaluate following. (a) 625 3/4 Solution (a) 625 3/4 Again, let's employ both forms to calculate this one. 625 3/4 =( 625 1/4 ) 3 =(5) 3 = 12
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