JEE Advance - Mathematics (1981 - No. 1)
Show that : $$\mathop {\lim }\limits_{n \to \infty } \left( {{1 \over {n + 1}} + {1 \over {n + 2}} + .... + {1 \over {6n}}} \right) = \log 6$$
The limit can be evaluated by recognizing it as a Riemann sum approximation of the integral of 1/x from 1 to 6.
The limit is equal to 6 times the limit of 1/n as n approaches infinity, which is 0.
The limit is a divergent series since the harmonic series diverges.
The limit can be directly computed by substituting infinity for n in each term.
The limit is undefined since the number of terms in the sum approaches infinity.
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