Question

1. Tunjukkan 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)
= 13k2
dst
maka . 1^2001 + 2^2001 + 3^2001 +...+ 2001^2001 = (2001^2001 + 1^2001) + (2000^2001 + 2^2001) + ...
= 13k1 +13k2 + ...
= 13(k1+k2+...)
= 13k
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