260 15 B, 1 3 3+ + 2+ + +33

Bài 16: Chứng minh rằng:

a,

2

+

2

²

+

2

³

+ +

... 2

⁶⁰

15

b,

1 3 3

+ +

²

+ + +

3

³

... 3

¹¹⁹

13

HD:

a, Ta có:

^{C= + + + +2 2}

²

²

³

^{... 2}

⁶⁰

^{= + + +}

(

^{2 2}

²

²

³

²

⁴

) (

^{+ 2}

⁵

^{+ +... 2}

⁸

)

^{+ +...}

(

²

⁵⁷

^{+ +... 2}

⁶⁰

)

( )

⁵

( )

⁵⁷

( )

C= + + + + + + + + + + + +

=>

^{C=15. 2 2}

(

^{+ + +}

⁵

^{... 2}

⁵⁷

)

2 1 2 4 8 2 1 2 4 8 ... 2 1 2 4 8

b, Ta có:

^{D= + +}

(

^{1 3 3}

²

) (

^{+ 3}

³

^{+ +3}

⁴

³

⁵

)

^{+ +...}

(

³

¹⁷

⁺³

¹⁸

⁺³

¹⁹

)

( )

3

17

3

17

13 3 .13 ... 3 .13 13 1 3 .... 3 13D= + + + = + + +