Question

chung minh rang

C=2+2^2+2^3+......+2^99+2^100 Chia het cho 31

Answer 1

C = 2 + 2² + 2³ + ... + 2⁹⁹ + 2¹⁰⁰

    = (2 + 2² + 2³ + 2⁴ + 2⁵) + ... + ( 2⁹⁶ + 2⁹⁷ + 2⁹⁸ + 2⁹⁹ + 2¹⁰⁰)

    = 62 + ... + 2⁹⁵.( 2 + 2² + 2³ + 2⁴ + 2⁵)

     = 62 + ... + 2⁹⁵ . 62

     = 62 . (1 + 2⁹⁵) chia hết cho 31

Answer 2

kudo shinichi khong dua ra ket qua ro rang