giải hô ạ A=2+2^2+2^3+2^4+…+2^2009 cm A chia het 21, 15

Đáp án:

Giải thích các bước giải:

A = 2+2∧2+2∧3+2∧4+……….+2∧1009

a) A chia hết 15

    A = 2+2∧2+2∧3+2∧4+……….+2∧1009

        =(2+2∧2+2∧3+2∧4)+(2∧5+2∧6+2∧7+2∧8)……….+ (2∧1006+2∧1007+2∧1008+2∧1009)

        = 2(1+2+4+8) + 2∧5(1+2+4+8)+………..+ 2∧1006 ( 1+2+4+8) 

        =2. 15 +2∧5.15+………….+ 2∧1006. 15

        = 15. (2+2∧5+……..+ 2∧1006)

     Vì 15 chia hết cho 15 ⇒ 15. (2+2∧5+……..+ 2∧1006) chia hết cho 15

b) A chia hết 21

    A = 2+2∧2+2∧3+2∧4+……….+2∧1009

        =(2+2∧2+2∧3+2∧4+2∧5+2∧6)+(2∧7+2∧8+2∧9+2∧10+ 2∧11+2∧12)+…+(2∧1004+2∧1005+2∧1006+2∧1007+2∧1008+2∧1009)

        = 2(1+2+4+8+16+32) + 2∧7(1+2+4+8+16+32)+………..+ 2∧1004 ( 1+2+4+8+16+32) 

        =2. 63 +2∧7.63+………….+ 2∧1004. 63

        = 63. (2+2∧7+……..+ 2∧1004)

     Vì 63 chia hết cho 21 ⇒ 21 (2+2∧7+……..+ 2∧1004) chia hết cho 21