[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
What is the simplified expression for 1/(√1+√2) + 1/(√
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- Max@Math Revolution
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=>
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
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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