[arabiakamal]

الحل التفصيلي:




S1=1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 +1/9 +1/10 + 1/11 +1/12 ..... unlimited series ....... eq1

S2=(S1)/2=1/4 +1/6 + 1/8 + 1/10 + 1/12 + ...unlimited series too.... eq2

S3=S1-S2=S1- (S1)/2=(S1/2)=S2=(1/2 -1/4)+(1/3 -1/6)+(1/4-1/8)+ (1/5 -1/10)+(1/6-1/12) +……….unlimited series eq3


بطرح eq3 - eq2 ينتج
S2-S2=0=(1/2-1/4-1/4)+(1/3-1/6-1/6)+(1/4-1/8-1/8)+(1/5-1/10-1/10
+...................
ًصفر = صفر