Final answer:
The siege of Yorktown was the last major battle of the Revolutionary War. General Cornwallis's surrender after being surrounded by American and French forces marked the end of major hostilities and led Britain to eventually recognize American independence with the Treaty of Paris.
Step-by-step explanation:
The last major battle of the Revolutionary War that convinced Britain the war was too difficult and costly to pursue was the siege of Yorktown. Led by General Charles Cornwallis, the British army was seeking a decisive victory in Virginia but instead found themselves surrounded by a combined force of over 9,500 American and 7,800 French troops. Cornwallis's last hope for breaking the siege was a failed breakout attempt across the York River. Eventually, he accepted Washington's terms of surrender, and on October 19, 1781, Cornwallis officially surrendered his army at Yorktown, marking the end of significant British military campaigns in the American colonies.
After Yorktown, British momentum in the war collapsed, and the Parliament of Great Britain voted to end military operations against the Americans. The Treaty of Paris was later signed in 1783, officially recognizing the independence of the original 13 colonies from Great Britain.
This decisive battle was not just a victory for the Americans and their allies but also signified the effective end of the Revolutionary War, as it prompted the British to negotiate peace and sealed the fate of the colonies' struggle for independence.