Question

Tentukan bahwa : 1^2001+2^2001+3^2001+........+2001^2001
adalah kelipatan 13

Answer 1

1^2001 + 2^2001 + 3^2001 +...+ 2001^2001= 13k
pandang : 2001^2001 + 1^2001 = (2001+1)(2001^2000 -20001^1999 ...+ 1) = 13 .54.(2001+1)(2001^2000 -2001^1999 ...+ 1) = 13.k1
2000^2001 + 2^2001 = (2000+2)(2000^2000 -2000^1999 ...+1)
= 13k2dst
maka . 1^2001 + 2^2001 + 3^2001 +...+ 2001^2001 = (2001^2001 + 1^2001) + (2000^2001 + 2^2001) + ...
=13k1 +13k2 + ...
=13(k1+k2+...)
= 13k