In a sign of growing optimism about the economy, community banks, credit unions and other lenders approved more small-business loan applications in January than in any other month during the past year.

Large banks, too, approved more loan requests in January than in prior months, though their overall percentage of approvals is well below that of other lenders, according to an analysis of lending trends released Thursday by Biz2credit, a New York firm that matches borrowers with lenders.

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