bySayantani Barman Experta en el extranjero
Question: What is \(\frac{1}{1*2}+\frac{1}{2*3}+\frac{1}{3*4}+\frac{1}{4*5}+\frac{1}{5*6}+\frac{1}{6*7}+\frac{1}{7*8}+\frac{1}{8*9}+\frac{1}{9*10}\)?
- \(\frac{2}{5}\)
- \(\frac{3}{5}\)
- \(\frac{7}{10}\)
- \(\frac{46}{55}\)
- \(\frac{9}{10}\)
Correct Answer: E
Approach Solution (1):
\(\frac{1}{1*2}+\frac{1}{2*3}+\frac{1}{3*4}+\frac{1}{4*5}+\frac{1}{5*6}+\frac{1}{6*7}+\frac{1}{7*8}+\frac{1}{8*9}+\frac{1}{9*10}\)
This can be rewritten as:
\([\frac{1}{1}-\frac{1}{2}]+[\frac{1}{2}-\frac{1}{3}]+[\frac{1}{3}-\frac{1}{4}]+[\frac{1}{4}-\frac{1}{5}]+[\frac{1}{5}-\frac{1}{6}]+[\frac{1}{6}-\frac{1}{7}]+[\frac{1}{7}-\frac{1}{8}]+[\frac{1}{8}-\frac{1}{9}]+[\frac{1}{9}-\frac{1}{10}]\)
Every term cancels out except
\([\frac{1}{1}-\frac{1}{10}]=\frac{9}{10}\)
Approach Solution (2):
\(\frac{1}{1*2}+\frac{1}{2*3}+\frac{1}{3*4}+\frac{1}{4*5}+\frac{1}{5*6}+\frac{1}{6*7}+\frac{1}{7*8}+\frac{1}{8*9}+\frac{1}{9*10}\)
Can be rewritten as:
0.5 + 0.166 + 0.083 + 0.05 + 0.03 + 0.023 + … ans so on (other values are too small)
Add them up
Sum = approximately 0.85 and a little more
Check option:
(A) \(\frac{2}{5}\)= 0.4
(B) \(\frac{3}{5}\)= 0.6
(C) \(\frac{7}{10}\)= 0.7
(D) \(\frac{46}{55}\)= 0.83
(E) \(\frac{9}{10}\)= 0.9 = Correct
“What is \(\frac{1}{1*2}+\frac{1}{2*3}+\frac{1}{3*4}+\frac{1}{4*5}+\frac{1}{5*6}+\frac{1}{6*7}+\frac{1}{7*8}+\frac{1}{8*9}+\frac{1}{9*10}\)?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills.
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