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For a positive integer n, f(n) is defined as 1 + 1/2 + 1/3 +

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For a positive integer n, f(n) is defined as 1 + 1/2 + 1/3 +

by Max@Math Revolution » Wed Oct 09, 2019 6:09 am
[GMAT math practice question]

For a positive integer n, f(n) is defined as 1 + 1/2 + 1/3 + ... + 1/n. What is the value of 10+f(1)+f(2)+...+f(9)?

A. f(11)
B. 9f(9)
C. 10f(10)
D. f(10)
E. 22
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by Max@Math Revolution » Thu Oct 10, 2019 11:41 pm
=>

10 + f(1) + f(2) + ... + f(9)
= 10 + ( 1 ) + ( 1 + 1/2 ) + ( 1 + 1/2 + 1/3 ) + ... + ( 1 + 1/2 + 1/3 + ... + 1/9 )
= 10 + 1*9 + (1/2)*8 + (1/3)*7 + ... + (1/8)*2 + (1/9)
= 10 + 1*(10 - 1) + (1/2)*(10-2) + (1/3)*(10-3) + ... + (1/8)*(10-8) + (1/9)(10-9)
= 10 + (-1) + (-1) + ... + (-1) + 10( 1 + 1/2 + 1/3 + ... + 1/9 )
= 1 + 10( 1 + 1/2 + 1/3 + ... + 1/9 )
= 10( 1 + 1/2 + 1/3 + ... + 1/9 + 1/10)
= f(10)

Therefore, D is the answer.
Answer: D
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