Question

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

a,Tính S

b,Chứng minh S\(⋮\)7

Answer 1

a) S = 3⁰ + 3² + 3⁴ + ..... + 3²⁰⁰²

9S = 3² + 3⁴ + ..... + 3²⁰⁰² + 3²⁰⁰⁴

9S - S = (3² + 3⁴ + ..... + 3²⁰⁰² + 3²⁰⁰⁴) - (3⁰ + 3² + 3⁴ + ..... + 3²⁰⁰²)

8S = 3²⁰⁰⁴ - 3⁰

S = \(\frac{3^{2004}-1}{8}\)

b) S = 3⁰ + 3² + 3⁴ + ..... + 3²⁰⁰²

S = (3⁰ + 3² + 3⁴) + (3⁶ + 3⁸  + 3¹⁰) + ..... + (3²⁰⁰⁰ + 3²⁰⁰¹ + 3²⁰⁰²)

S = (1 + 9 + 81) + 3⁶.(1 + 9 + 81) + ..... + 3²⁰⁰⁰.(1 + 9 + 81)

S = 91 + 3⁶ . 91 + ...... + 3²⁰⁰⁰ . 91

S = 91 . (1 + 3⁶ + ...... + 3²⁰⁰⁰)

S = 7 . 13 . (1 + 3⁶ + ...... + 3²⁰⁰⁰)

Answer 2

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