Question

Ex.. 25 si ex...........41 va rog dau coroana

Answer 1

25. N=5²+5^4 +...+5^1992=
=5²(1+5²+5^4+....+5^1990)=
=5²[(1+5²)+5^4·(1+5²)+....+5^1988·(1+5²)]
=5²·(1+5²)(1+5^4+...+5^1988)=25·26(1+5^4+.....+5^1988)=5·130·(...)
⇒N divizibil cu 130
41.A=3^(2n+1)·5^(3n+2)-(3²)^(n+1)·5^(3n+1)=
=3^(2n+1)·5^(3n+2)-3^(2n+2)·5^(3n+1)=
=3^(2n+1)·5^(3n+1)·[5-3]=
=2·3²·5[3^(2n-1)·5^3n]=
=90·[3^(2n-1)·5^3n] divizibil cu 90