limn ( (n+1)^ 13n^ 43+ (n+2)^ 13n^ 43+ …+ (2n )^ 13n^ 43) is equal to :

Question

Accepted Answer

Correct answer: A. (a) JEEN Main 2019 limn ( (n+1)^ 13+(n+2)^ 13+ …+(n+n)^ 13n (n )^ 13 ) = limn (n+r)^ 13n .n^ 13 = (1+x)^ 13 dx ( ∵ rn x and 1n dx) = ( 34(1+x)^ 43 )_0^1= 34 (2 )^ 43- 34

$lim n \to \infty (\frac{( n + 1 ) ^{\frac{1}{3}}}{n ^{\frac{4}{3}}} + \frac{( n + 2 ) ^{\frac{1}{3}}}{n ^{\frac{4}{3}}} + \dots + \frac{( 2 n ) ^{\frac{1}{3}}}{n ^{\frac{4}{3}}}) is equal to :$

Solution

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