let x=1+a+a2+.............. y=1+b+b2+.......... thn prove that 1+ab+a2b2+.......=xy/x+y-1 Share with your friends Share 39 Priyanka Kedia answered this Given, x=1+a+a2+......∞Since this is a infinite G.P. series, where, (first term)=1 and common difference=a,So,x=11-a⇒x-ax=1⇒ax=x-1⇒a=x-1xSimilarly,y=1+b+b2+......∞ is a infinite G.P. series, where, (first term)=1 and common difference=b,So,y=11-b⇒y-by=1⇒by=y-1⇒b=y-1yAnd now,L.H.S.=1+ab+a2b2+....∞ =11-ab infinte G.P. series where (first term)=1 and common difference=ab =11-x-1xy-1y =xyxy-xy+x+y-1 =xyx+y-1 =R.H.S.Hence Proved. 138 View Full Answer