Practice problem
Does the sequence an=1n+1n+1+⋯+12na_n = \frac1n+\frac1{n+1}+\dots+\frac1{2n}an=n1+n+11+⋯+2n1 converge to a real number? If so, evaluate the limit. If not, elaborate.
Yes, and the limit is exactly ln2\ln2ln2.
No, because the harmonic series diverges.
No. It converges to an imaginary number.
No. Even though the sequence is close to ln2\ln2ln2 for large values of nnn, the terms oscillate too much for the limit to exist.
Type a concept, like “slope” or “photosynthesis”.