Question

A=2+2 mũ 2+2 mũ 3+.....+2 mũ 99+2 mũ 100

B=1+5+5 mũ 2+5 mũ 3+......+5 mũ 99+5 mũ 100

Answer 1

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Answer 2

    A  = 2 +  2² + 2³ +...+2⁹⁹ + 2¹⁰⁰

   2A  =       2² + 2³ +...+ 2⁹⁹ + 2¹⁰⁰ + 2¹⁰¹

2A - A =      2¹⁰¹ - 2

   A      = 2¹⁰¹ - 2

 

Answer 3

  B        =  1 + 5 + 5² + 5³ +...+ 5⁹⁹ + 5¹⁰⁰

5B        =       5 + 5² + 5³ +...+ 5⁹⁹ + 5¹⁰⁰ + 5¹⁰¹

5B - B   =  5¹⁰¹ - 1

   4B     = 5¹⁰¹ - 1

     B      = \(\dfrac{5^{101}-1}{4}\)

     B     = 

Answer 4

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Answer 5

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