[math-fun] Two sums

hello I noticed that: for some values of a and b... theta=(1/b)*sum(((-1)^(n+1)/n)*(sin(b*theta)/sin(a*theta))^n*sin(n*theta*(b+a)),n=1..inf) ; I have deducted: theta=(sum(((-1)^(n+1)*(sinh(b*theta))^n*sinh((b+a)*n*theta))/(n*(sinh(a*theta))^n),n=1..inf))/b; an example : a=1/15 ; b= 1/30 ; theta = Pi FME...