Hello... At his request, I sent the following lines to a friend sum(2^k*tan(2^k*x),k=0..n)=cot(x)-2^(n+1)*cot(2^(n+1)*x); sum(2^k*tanh(2^k*x),k=0..n)=-coth(x)+2^(n+1)*coth(2^(n+1)*x); tanh(2*x)=2/(coth(x)+2/(coth(x/2)+2/(coth(x/4)+2/(coth(x/8)+2/(coth(x/16)+2/(coth(x/32)+2/(coth(x/64)+2/(coth(x/128)+2/(coth(x/256)+2/cdots))))))))); tan(2*x)=2/(cot(x)-2/(cot(x/2)-2/(cot(x/4)-2/(cot(x/8)-2/(cot(x/16)-2/(cot(x/32)-2/(cot(x/64)-2/(cot(x/128)-2/(cot(x/256)-2/cdots))))))))); I do not know if she understood anything about it.finally she had a good time. FME...