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Using term-by-term integration of 1/(1-t)=Σ_{n=0}∞tn, which value is represented by Σ_{n=0}∞ (1/2)n+1/(n+1)?

Using term-by-term integration of 1/(1-t)=Σ_{n=0}∞tⁿ, which value is represented by Σ_{n=0}∞ (1/2)ⁿ⁺¹/(n+1)?