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What is the simplified expression for 1/(√1+√2) + 1/(√

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What is the simplified expression for 1/(√1+√2) + 1/(√

by Max@Math Revolution » Fri Apr 05, 2019 12:38 am

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[GMAT math practice question]

What is the simplified expression for 1/(√1+√2) + 1/(√2+√3) + 1/(√3+√4) + ... + 1/(√99+√100)?

A. 8
B. 9
C. 10
D. 11
E. 12
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by Max@Math Revolution » Sun Apr 07, 2019 5:35 pm
=>

1/(√1+√2) + 1/(√2+√3) + 1/(√3+√4) + ... + 1/(√99+√100)
=1/(√2+√1) + 1/(√3+√2) + 1/(√4+√3) + ... + 1/(√100+√99)
= (√2-√1)/{(√2+√1)(√2-√1)} + (√3-√2)/{(√3+√2)(√3-√2)} + (√4-√3)/{(√4+√3)(√4-√3)} + ... + (√100-√99)/{(√100+√99)(√100-√99)}
= (√2-√1) + (√3-√2) + (√4-√3) + ... + (√100-√99)
= (-√1+√2) + (-√2+√3) + (-√3+√4) + ... + (-√99+√100)
= -1+10
= 9

Therefore, the answer is B.
Answer: B
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