WEBVTT
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the problem is use the following steps to prove 17
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17 is one plus X to the power of K
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is equal to some from zero to infinity. K
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n times X to the power of n Here's the
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up up psuedo facts is less than one part a
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. That gearbox is equal to the series k N
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X to end differentiate this series to show that the
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derivative of G well X is equal to K times
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GLX over one plus x here. Absolutely. If
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X is less than one, so behalf she x
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problem is equal to some from one to finally and
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times K and hams x two in my squad.
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Then we compute G of X prom hands one plus
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x, which is equal to some and from one
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to infinity. End times k n times x two
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m 11 as x two n And then we can
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rewrite this series as some and from zero to infinity
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10 times K and us and plus one times Hey
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, Paswan hams extra m Then we compute and times
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k n plus plus one Homs a M plus one
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. So by definition, this is equal to 10
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times. Hey, Hams K minus one times dot
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a dot times k minus And once one over in
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factorial us and as one harms Hey, times K
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minus one. I'm started all times K minus in
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over and plus one bacteria which is equal to K
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hams, came minus one. I'm started all times
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K minus in minus one. Offer a bacterial hams
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in plus a minus n which is a co two
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. Hey, hams. Mhm. So for half
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this is equal to Assam and from zero to infinity
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. Okay, Tom's K in hands X to end
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, which is equal to K Jail Fox. Yeah
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. So approved this equation Hard to be let h
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of X is equal to one plus X to the
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power of negative K video box and showed that HX
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prom is equal to zero. So we have HX
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crown is equal to negative K and spawn plus X
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the power of negative K minus one times to lux
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plus one plus x two negative K hams, the
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derivative of jacks. And if we use the result
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in part of a So this is hey hams.
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So you will g wax over one plus x so
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we can say this is a cultural zero sense this
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term. It's just K times one plus x to
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the powerful negative K minus one hams gearbox. Part
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of C deduced that gearbox is a go to one
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plus X to the power of K. So from
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part B, we have geo vax is equal to
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some constant number. C If we liked, X
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is equal to zero Behalf h zero it is c
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is equal to h zero is a cultural one times
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one which is a good one over half HX is
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0 to 1, so Geo box is equal to
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one plus X to the power of K.