Question

SO SÁNH

A=1000¹⁰⁰¹

B=1¹+2²+3³+4⁴+...+1000¹⁰⁰⁰

Answer 1

Ta có:

1¹ < 1000¹⁰⁰⁰

2² < 1000¹⁰⁰⁰

3³ < 1000¹⁰⁰⁰

....

999⁹⁹⁹ < 1000¹⁰⁰⁰

1000¹⁰⁰⁰ = 1000¹⁰⁰⁰

=> B = 1¹ + 2² + 3³ + ...+ 999⁹⁹⁹ + 1000¹⁰⁰⁰ < 1000¹⁰⁰⁰ + ...+ 1000¹⁰⁰⁰ (Có 1000 số 1000¹⁰⁰⁰)  

=> B < 1000.1000¹⁰⁰⁰ = 1000¹⁰⁰¹ = A

Vậy B < A

Answer 2

Ta có:

1¹ < 1000¹⁰⁰⁰

2² < 1000¹⁰⁰⁰

............

999⁹⁹⁹ < 1000¹⁰⁰⁰

1000¹⁰⁰⁰ = 1000¹⁰⁰⁰

=> B = 1¹ + 2² + 3³ + ...+ 999⁹⁹⁹ + 1000¹⁰⁰⁰ < 1000¹⁰⁰⁰ + ...+ 1000¹⁰⁰⁰ (Có 1000 số 1000¹⁰⁰⁰)  

<=> B < 1000.1000¹⁰⁰⁰ = 1000¹⁰⁰¹ = A

Vậy.................

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