If lim n → ∞ ∑ r = n 2 n r 3 r 4 + n 4 n 4 = a − b , find 32 b / a − 10 .

Start Free Mock LoginAlready registered? Login here

Mathematics - Definite Integration Question with Solution | TestHub

MathematicsDefinite IntegrationSum of series using definite integrationHard2 minQB

MathematicsHardinteger

If $lim_{n \to \infty} \sum_{r = n}^{2 n} \frac{n ^{4}}{r ^{3} r ^{4} + n ^{4}} = a - b$ , find $32 b / a - 10$ .

Answer:

Solution:

This is the Riemann integral $\int_{1}^{2} d x / [x^{3} x^{4} + 1]$ . With $u = 1/ x^{2}$ , it evaluates to $1/2 - 17 /8 = (4 - 17) /8$ . Thus $a = 1/2, b = 17/64$ , giving $32 b / a - 10 = 7$ .

Stream:JEESubject:MathematicsTopic:Definite IntegrationSubtopic:Sum of series using definite integration

⏱ 2mℹ️ Source: QB

Doubts & Discussion

Loading discussions...