a) Thu gọn A

Lời giải:

a) 25A =  5⁵² – 5⁵⁰ + 5⁴⁸ – 5⁴⁶ + … + 5⁸ – 5⁶ + 5⁴ – 5²

Suy ra: 25A + A = 5⁵² – 1

Suy ra: 26A = 5⁵² – 1

Suy ra: A = \(\frac{{{5^{52}}--{\rm{ }}1}}{{26}}\)

b) Từ câu a) suy ra: 26.A + 1 = 5⁵²

Suy ra: n = 52

c) A = (5⁵⁰ – 5⁴⁸) + (5⁴⁶ – 5⁴⁴) + … + (5⁶ – 5⁴) + (5² – 1)

A = 5⁴⁸.(5² – 1) + 5⁴⁴.(5² – 1) + … + 5⁴.(5² – 1) + (5² – 1)

A = 5⁴⁸.24 + 5⁴⁴.24 + … + 5⁴.24 + 24

A = 5⁴⁷.25.24 + 5⁴³.25.24 + … + 5³.25.24 + 24

A = 5⁴⁷.600 + 5⁴³.600 + … + 5³.600 + 24

A = 5⁴⁷.6.100 + 5⁴³.6.100 + … + 5³.6.100 + 24

A = 100.( 5⁴⁷.6 + 5⁴³.6 + … + 5³.6) + 24

Suy ra A chia cho 100 dư 24.