If 2a1,2b1,a!=b, then the value of ((a-1)-(1)

Question

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)-...)

Aditya Gupta · Accepted Answer

put a-1=x and b-1=ythen 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/lnbkindly approve :)

Algebra> If 2>a>1,2>b>1,a!=b, then the value of ((...

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

Aditya Gupta

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Algebra> If 2>a>1,2>b>1,a!=b, then the value of ((...

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

Aditya Gupta

LIVE ONLINE CLASSES

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