Question

[Phạm Thị Minh Ánh]

Cho S = 3⁰+3²+3⁴+3⁶+....+3²⁰⁰²

a)Tính S

b ) Chứng minh S chia hêts cho 7

Answer 1

[dinhkhachoang]

S=\(3^0+3^2+3^4+3^6+.....+3^{2002}\)

3S=\(3^2+3^4+3^6+.....+3^{2002}+3^{2003}\)

3S-S=\(\left(3^2+3^4+3^6+....+3^{2002}+3^{2003}\right)-\left(3^0+3^2+3^4+3^6+....+3^{2002}\right)\)

S=\(3^{2003}-3^0\)