This gives the meaning of the terms as generally understood in the middle of the 18th century. Robert Hooper's Physician's Vade-Mecum, published in 1812 has been used as a source of terms in the early 19th century; many of the terms mentioned are still in common use.
In either case, the value at x = 0 is defined to be the limiting value sinc(0) = 1. The normalization causes the definite integral of the function over the real numbers to equal 1 (whereas the same integral of the unnormalized sinc function has a value of Ï).
These are called harmonic numbers. Then your sum is $H_{100}-\frac{1}{2}H_{50}-1$. If you're happy with an approximation, we know that $H_k\approx \ln k + \frac{1}{2k}+\gamma$, where $\gamma\approx 0.5772156$. Hence your answer is approximately $\ln 100 + \gamma-0.5 \ln 50 -\frac{\gamma}{2}-1\approx 1.93776648$.