The given dicarboxylic acid (HOOC(CH2)nCOOH) undergoes cyclisation on heating alone to form a cyclic anhydride. Let's analyze this reaction and determine the minimum value of n required for cyclisation to occur.

1. Formation of cyclic anhydride:
When heated, the dicarboxylic acid molecule undergoes intramolecular dehydration, resulting in the formation of a cyclic anhydride. This process involves the elimination of a water molecule from the carboxylic acid groups.

2. Intramolecular dehydration:
Intramolecular dehydration occurs when a water molecule is eliminated from within the same molecule. The carboxylic acid groups in the dicarboxylic acid molecule can undergo dehydration to form the cyclic anhydride. This process is favorable when the formation of the cyclic anhydride is more stable compared to the reactant dicarboxylic acid.

3. Stability of cyclic anhydride:
In order for the cyclisation to occur, the cyclic anhydride formed must be more stable than the dicarboxylic acid. The stability of an anhydride depends on factors such as ring strain, resonance stabilization, and conjugation. A cyclic anhydride with a smaller ring size is generally more stable.

4. Minimum value of n:
To determine the minimum value of n required for cyclisation, we need to consider the ring size of the resulting cyclic anhydride. A 5-membered ring is considered relatively stable, while a 4-membered ring is highly strained. Therefore, the minimum value of n should be such that it forms a 5-membered ring in the cyclic anhydride.

5. n = 2:
When n = 2, the dicarboxylic acid becomes HOOC(CH2)2COOH. On heating, this compound undergoes intramolecular dehydration, eliminating a water molecule to form a cyclic anhydride. The resulting cyclic anhydride has a 5-membered ring, which is relatively stable.

6. Conclusion:
Hence, the minimum value of n required for the dicarboxylic acid to undergo cyclisation and form a stable cyclic anhydride is 2.