Solve: limn→∞{1n+1+1n+2+…+12n}=
Given,
limn→∞{1n+1+1n+2+…+12n}
=nlim→∞n∑r=11n+r
=nlim→∞n∑r=11n⋅(11+rn)
It is in the form of
nlim→∞n∑r=11nf(rn)=∫1011+xdx
⇒∫1011+xdx=[log(1+x)]10
∴log2−log1=log(2)