# #17 of March 2015 Grade 11 - Natural Sciences & Liberal Arts CSAT (Korean SAT) Mock test

Algebra Level 4

A sequence $$\{a_n\}$$ satisfies $$a_1=1$$ and $$\dfrac{a_{n+1}}{n+2}=\dfrac{a_n}{n}+\dfrac{1}{2}$$ for all natural numbers $$n.$$

Let $$S = \dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{5}+\cdots+\dfrac{1}{102}.$$

Find the value of $$\boxed{a_{103}-5356S}.$$

This problem has been modified by me, and is a part of <Grade 11 CSAT Mock test> series.

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