The city of Providence, R.I., yesterday sued a unit of Xerox Corp., saying that it had underestimated by about $10 million how much the city would save when it renegotiated its pension benefits last year, Reuters reported yesterday. Providence charged in court papers that as it negotiated the terms of changes to its pension benefits with workers and retirees in 2012, the Buck Consultants arm of Xerox failed to account for a cost-of-living adjustment paid to retirees during the negotiations. The error will cost the capital of the smallest U.S. state, which narrowly avoided bankruptcy last year in part due to Mayor Angel Taveras' deal to cut its pension obligations, some $10 million over 28 years. Providence faced about $900 million in unfunded pension obligations when it entered the negotiations and had expected to cut that liability by about $165 million through the pension deal, the city said in papers filed in U.S. District Court in Providence.