Question

[Leo unique]

chứng minh răng A chia hết cho 97 biết A=(1/1.2+1/3.4+1/5.6+....+1/63.64).33.34.35.....64

Answer 1

[Jin Air]

Gọi 1/1.2 + 1/3.4 + ... + 1/63.64 là B

Ta có:

B= 1/1.2 + 1/3.4 + ... + 1/63.164

B=1-1/2+1/3-1/4+...+1/63-1/64

=1+1/2+1/3+1/4+...+1/63+1/64 - 2.(1/2+1/4+1/6+...+1/64)

=1+1/2+1/3+1/4+...+1/63+1/64-1-1/2-1/3-...-1/32

=1/33+1/34+1/35+...+1/64

=(1/33+1/64)+(1/34+1/63)+...+(1/48+1/49)

=97/33.64 + 97/34.63 + .... + 97/48.49

=97(1/33.64+1/34.63+...+1/48.49)

=97k

Thay vào B vào A ta được

97k.33.34.35...64 chia hết cho 97

 vậy A chia hết 97

Answer 2

[l҉o҉n҉g҉ d҉z҉]

Gọi 1/1.2 + 1/3.4 + ... + 1/63.64 là B Ta có: B= 1/1.2 + 1/3.4 + ... + 1/63.164 B=1-1/2+1/3-1/4+...+1/63-1/64 =1+1/2+1/3+1/4+...+1/63+1/64 - 2.(1/2+1/4+1/6+...+1/64) =1+1/2+1/3+1/4+...+1/63+1/64-1-1/2-1/3-...-1/32 =1/33+1/34+1/35+...+1/64 =(1/33+1/64)+(1/34+1/63)+...+(1/48+1/49) =97/33.64 + 97/34.63 + .... + 97/48.49 =97(1/33.64+1/34.63+...+1/48.49) =97k Thay vào B vào A ta được97k.33.34.35...64 chia hết cho 97 vậy A chia hết 97