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Question

loge[(1+x)1+x(1x)1x]=a(x21.2+x43.4+x65.6+...)
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Solution

loge[(1+x)1+x(1x)1x]


=loge(1+x)1+x+loge(1x)1x


=(1+x)loge(1+x)+(1x)loge(1x)


=[loge(1+x)+loge(1x)]+x[log(1+x)log(1x)]


=loge(1x2)+xloge(1+x1x)


=(x2x42x63....)+2x(x+x33+x55+...)


=(x2x42x63...)+(2x2+2x33+2x55+....)


=(x2+x43.2+x65.3+...)


=2(x21.2+x43.4+x65.6+...)


a=2


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