If x > 1,y > 1,z > 1 are in G.P. then 1/1 + lnx,1/1 + lny,n 1/1 + lnz are in

(b) : Let the common ratio of the G.P. be r, then y=x r and z=x r^2 ln y=ln x+ln r, and ln z=ln x+2 ln rn(1 / 1+ln x)=(1 / A), (1 / 1+ln y)=(1 / A+D) and (1 / 1+ln z)=(1 / A+2 D) Hence (1 / 1+ln x), (1 / 1+ln y), (1 / 1+ln z) are in H.P.

If x > 1,y > 1,z > 1 are in G.P. then 1/1 + lnx,1/1 + l... | Sequence & Series (Mathematics)

(b) : Let the common ratio of the G.P. be

r

, then

y=x r

and

z=x r^2 \ln y=\ln x+\ln r

, and

\ln z=\ln x+2 \ln r

\frac{1}{1+\ln x}=\frac{1}{A}, \frac{1}{1+\ln y}=\frac{1}{A+D}

and

\frac{1}{1+\ln z}=\frac{1}{A+2 D}

Hence

\frac{1}{1+\ln x}, \frac{1}{1+\ln y}, \frac{1}{1+\ln z}

are in H.P.

Explanation

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