Tìm chữ số tận cùng của S = 3 x 13 x 23 x 33 x ... x 2013

Phương pháp giải

- Ta có tích của 4 thừa số có tận cùng là 3 thì cho chữ số tận cùng là 1. - Tìm số thừa số của tích đã cho - Lấy số số hạng của dãy : 4, từ đó tìm được chữ số tận cùng của tích đã cho.

Lời giải của GV ufaindo.xyz

Dãy trên gồm các thừa số có tận cùng là 3 Số các thừa số trong tích trên là (2013 – 3) : 10 + 1 = 202 (số) Ta có 3 x 3 x 3 x 3 = 81 nên tích của 4 thừa số có tận cùng là 3 thì cho chữ số tận cùng là 1. Mà 202 : 4 = 50 (dư 2) Vậy 202 thừa số được chia thành 50 nhóm (Mỗi nhóm gồm 4 thừa số) và dư 2 thừa số. Xét tích các chữ số tận cùng của các thừa số:

Mỗi nhóm đều có tận cùng bằng 1. Vậy S có chữ số tận cùng là 9

Báo lỗi - Góp ý

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