After weeks of missteps that left frustrated residents struggling to sign up for COVID-19 shots, there are increasing signs the Massachusetts vaccination campaign is gaining momentum.

The number of doses injected have jumped by nearly 40 percent since the start of the month, to more than 910,000 so far, state figures released Tuesday show, marking the strongest period yet in a rollout that began in mid-December. Just a week after they became eligible, more than 46 percent of the state’s roughly 430,000 residents 75 and older already have been vaccinated.

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