Try this beautiful problem from the Pre-RMO, 2017 based on Series.

Series Problem – PRMO 2017

Let the sum \(\displaystyle\sum_{n=1}^{9}\frac{1}{n(n+1)(n+2)}\) written in its lowest terms be \(\frac{p}{q}\), find the value of q-p.

  • is 107
  • is 83
  • is 840
  • cannot be determined from the given information

Key Concepts



Rearrangement of terms in series

Check the Answer

But try the problem first…

Answer: is 83.

Suggested Reading

PRMO, 2017, Question 6

Calculus Vol 1 and 2 by Apostle

Try with Hints

First hint

here \(\displaystyle\sum_{n=1}^{9}\frac{n+2-n}{2n(n+1)(n+2)}\)


Second Hint




Final Step

\(\Rightarrow \frac{27}{110}\)

\(\Rightarrow q-p=110-27\)


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