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What is the value of 1 / (√2+√1) + 1 / (√3+√2) + 1/(

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What is the value of 1 / (√2+√1) + 1 / (√3+√2) + 1/(

by Max@Math Revolution » Wed Jun 19, 2019 11:54 pm

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[GMAT math practice question]

What is the value of 1 / (√2+√1) + 1 / (√3+√2) + 1/(√4+√3) + ... + 1/(√25+√24)?

A.1
B. 2
C. 3
D. 4
E. 5
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by GMATGuruNY » Thu Jun 20, 2019 2:18 am
Max@Math Revolution wrote:[GMAT math practice question]

What is the value of 1 / (√2+√1) + 1 / (√3+√2) + 1/(√4+√3) + ... + 1/(√25+√24)?

A.1
B. 2
C. 3
D. 4
E. 5
1/(√2+√1)

= [(1)(√2-√1)] / [(√2+√1)(√2-√1)]

= (√2-√1)/(2-1)

= √2-√1

By extension, the given expression becomes:
(√2-√1) + (√3-√2) + (√4-√3) +...+ (√24-√23) + (√25-√24)

The red values all cancel out, yielding the following:
-√1 + √25 = -1 + 5 = 4

The correct answer is D.
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by Max@Math Revolution » Sun Jun 23, 2019 5:14 pm
=>

We rationalize the denominator of each fraction to give
1 / (√2+ √1) + 1 / (√3+ √2) + 1/( √4+ √3) + ... + 1/( √25+ √24)
= (√2-√1)/[(√2+√1)(√2-√1)] + (√3-√2)/[(√3+√2) (√3-√2)] + (√4-√3)/[(√4+√3) (√4-√3)] + ... + (√25-√24)/[(√25+√24)(√25-√24)]
= (√2-√1)/[2-1] + (√3-√2)/[3-2] + (√4-√3)/[4-3] + ... + (√25-√24)/[25 - 24]
= (√2-√1) + (√3-√2) + (√4-√3) + ... + (√25-√24)
= √25 - √1 = 5 - 1 = 4


Therefore, the answer is D.
Answer: D
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