Find the integer closest to a &#x2212;<!-- − --> b Let a = 1 <mro

aniawnua

aniawnua

Answered question

2022-05-22

Find the integer closest to a b
Let
a = 1 2 1 + 2 2 3 + 3 2 5 + + 1001 2 2001 .
Let
b = 1 2 3 + 2 2 5 + 3 2 7 + + 1001 2 2003 .
Then, what is the closest integer of ( a b )?

Answer & Explanation

Erzrivalef6

Erzrivalef6

Beginner2022-05-23Added 10 answers

We have
a b = k = 1 1001 k 2 2 k 1 k = 1 1001 k 2 2 k + 1 = 1 2 1 1001 2 2003 + k = 1 1000 ( k + 1 ) 2 k 2 2 k + 1 = 1 2 1 1001 2 2003 + k = 1 1000 1 = 1001 1001 2 + 1 1001 1001 1001 2 ( 1 1 2002 ) = 500 3 4
Denisse Valdez

Denisse Valdez

Beginner2022-05-24Added 5 answers

a b = i = 1 1001 ( i 2 2 i 1 i 2 2 i + 1 ) = i = 1 1001 2 i 2 4 i 2 1 = 1 2 i = 1 1001 4 i 2 1 4 i 2 1 + 1 2 i = 1 1001 1 4 i 2 1 a b = 1001 2 + 1 4 i = 1 1001 ( 1 2 i 1 1 2 i + 1 ) = 1001 2 + 1 4 ( 1 1 2003 )

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