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$The value of lim_{n \to \infty} [\frac{1}{n a} + \frac{1}{n a + 1} + \frac{1}{n a + 2} + \dots + \frac{1}{n b}] is$

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detailed solution

Correct option is C

the given limitL=limn→∞ 1na+1na+1+1na+2+⋯+1na+n(b−a)=limn→∞ ∑r=0(b−a)n 1na+r=limn→∞ 1n∑r=0(b−a)n 1a+r/n=∫0(b−a) dxa+x=[log⁡(a+x)]0b−a=log⁡b−log⁡a=log⁡(b/a)

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The value of limn→∞ 1na+1na+1+1na+2+⋯+1nb is

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$The value of lim_{n \to \infty} [\frac{1}{n a} + \frac{1}{n a + 1} + \frac{1}{n a + 2} + \dots + \frac{1}{n b}] is$