One day Niloy, a friend of Gourab gave Gourab some questions relating to series.

A series was: $$1+2+2+3+3+3+4+4+4+4+\dots$$ Niloy then added a twist. He told Gourab that he doesn't need to do anything with this series but he must make another series with the reciprocals of each term of the given series and find the sum of first $55$ terms.

What was the answer of Niloy's question?

A series was: $$1+2+2+3+3+3+4+4+4+4+\dots$$ Niloy then added a twist. He told Gourab that he doesn't need to do anything with this series but he must make another series with the reciprocals of each term of the given series and find the sum of first $55$ terms.

What was the answer of Niloy's question?