<transcript><audio_32>transform of T to the power and so you can use Laplace transform T term of T to the power 0 to compute the present form of T plus s form of T plugin Inc I plug in N equals 1 the present form of T</transcript><transcript><audio_33>equals 1 over s times the Laplace transform of 1 so you get 1 over s squared the platform of T squared plug in N equals 2 because 2 over s times the previous Laplace transform so 2 of s</transcript><transcript><audio_34>times 1 over s squared so 2 over X cubed the next one you will get 3 over s times 2 over s cube so 3 times 2 over s to the power 4 they will get 4 over s times T to the 3 over s cube so 2 times 3 times</transcript><transcript><audio_35>4 over a to the power 5 etc etc and then you observed a pattern of course in numerator well we will get an N factorial for the full 3 times 2 or n times 1 etc and in the numerator you get at a super</transcript> transform of T to the power and so you can use Laplace transform T term of T to the power 0 to compute the present form of T plus s form of T plugin Inc I plug in N equals 1 the present form of T equals 1 over s times the Laplace transform of 1 so you get 1 over s squared the platform of T squared plug in N equals 2 because 2 over s times the previous Laplace transform so 2 of s times 1 over s squared so 2 over X cubed the next one you will get 3 over s times 2 over s cube so 3 times 2 over s to the power 4 they will get 4 over s times T to the 3 over s cube so 2 times 3 times 4 over a to the power 5 etc etc and then you observed a pattern of course in numerator well we will get an N factorial for the full 3 times 2 or n times 1 etc and in the numerator you get at a super
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