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What is the value of 23·5 + 25·7 + 27·9 + 29·11 + 211·13?

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by Max@Math Revolution » Tue Aug 04, 2020 2:22 am
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[GMAT math practice question]

What is the value of $$\frac{2}{3·5}+\frac{2}{5·7}+\frac{2}{7·9}+\frac{2}{9·11}+\frac{2}{11·13}$$ ?

A. 2/27
B. 3/29
C. 5/33
D. 9/37
E. 10/39
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Re: What is the value of 23·5 + 25·7 + 27·9 + 29·11 + 211·13?

by Max@Math Revolution » Thu Aug 06, 2020 2:37 am
=>

Remember that 2/n(n + 2) = 1/n – 1/n + 2.
2/3·5 + 2/5·7 + 2/7·9 + 2/9·11 + 2/11·13
= (1/3 – 1/5) + (1/5 – 1/7) + (1/7 – 1/9) + (1/9 – 1/11) + (1/11 – 1/13)
= 1/3 – 1/13
= (13 - 3)/(3·13) = 10/39

Therefore, E is the correct answer

Answer: E.
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