Flag Algebra> If 2>a>1,2>b>1,a!=b, then the value of ((...
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If 2>a>1,2>b>1,a!=b, then the value of ((a-1)-(1)/(2)(a-1)^(2)+(1)/(3)(a-1)^(3)-...)/((b-1)-(1)/(2)(b-1)^(2)-(1)/(3)(b-1)^(3)-...)

Gaurav Shukla , 6 Years ago
Grade 12th pass
anser 1 Answers
Aditya Gupta

Last Activity: 6 Years ago

put a-1=x and b-1=y
then x and y both are less than 1.
let f(z)= z – z^2/2+z^3/3 – ….
now, we have to find the value of f(x)/f(y)
however, we all know the series expansion of ln(1+z) is precisely  z – z^2/2+z^3/3 – …. as this is a standard result so that f(z)= ln(1+z).
so f(x)/f(y)= ln(1+x)/ln(1+y)= lna/lnb
kindly approve :)

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