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log(1-x)=-x-x²/2-x³/3-x⁴/4-......... for x<1

Differentiate it we get

-1/(1-x)=-1-x-x²-x³-x⁴-...... for x<1

Or

1/1-x)=1+x+x²+x³+x⁴+......

now put x=-1 we get

1/2=1-1+1-1+1-1+1-1+.........

It is true or not????