Question

stabiliti daca 54 divide m+n in cazul : m= 2/4+1/3+2/8 +1/5+2/12+1/7+....+3 la puterap+1/5997•3 la puterea p si n=1/2+4/6+8/10+5/6+12/14+7/8+....+1998/1999 .iar p€N(va rog mersi)

Answer 1

m=2/4+1/3+2/8 +1/5+2/12+1/7+....+[3^(p+1)]/(5997x3^p)=
=1/2+1/3+1/4+1/5+1/6+1/7+...+3/5997=
=1/2+1/3+1/4+1/5+1/6+1/7+...+1/1999, unde ''^''= la puterea
Deci m=1/2+1/3+1/4+1/5+1/6+1/7+...+1/1999
si ''m'' are 1999-2+1=1998 termeni
n=1/2+4/6+8/10+5/6+12/14+7/8+...+1998/1999=
=1/2+2/3+3/4+4/5+5/6+6/7+7/8+...+1998/1999
Deci n=1/2+2/3+3/4+4/5+5/6+6/7+7/8+...+1998/1999
si ''n'' are 1999-2+1=1998 termeni

m+n=
=1/2+ 1/3+ 1/4+ 1/5+ 1/6+ 1/7+ 1/8+ ... +1/1999+
+1/2+2/3+3/4+4/5+5/6+6/7+7/8+...+1998/1999=
=(1/2+1/2)+(1/3+2/3)+(1/4+3/4)+1/5+4/5)+(1/6+5/6)+(1/7+6/7)+...+
+(1/1999 +1998/1999)=1+1+1+1+1+...(de 1998 de ori)...+1=1998

m+n=1998