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Expand ln(1+x) and ln(1-x) and hence deduce that

ln((y+1)/(y-1))=[2/y]+[2/(3(y^3))]+[2/(5(y^5))]+[2/(7(y^7))]. State the range of values of y for which the expansion is valid. Hence calculate ln(101) correct to 4 significant figures given that ln(99)=4.59507.

I managed to expand ln(1+x) and ln(1-x). Can someone help me to continue the problem?

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