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Constant

For a∈ R th...

Question

For $a \in R$ (the set of all real numbers), $a \neq - 1$ . ${lim}_{n \to \infty} \frac{(1^{a} + 2^{a} + . . . . . . + n^{a})}{{(n + 1)}^{a - 1} [(n a + 1) + (n a + 2) + . . . . . . . + (n a + n)]} = \frac{1}{60}$ , then $a =$

A

5

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B

7

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C

\frac{- 15}{2}

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D

- \frac{17}{2}

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Solution

The correct options are
B $7$
D $- \frac{17}{2}$

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a

\in R

(the set of all real numbers),

a \neq - 1, lim n \to \infty \frac{(1^{a} + 2^{a} + \dots + n^{a})}{(n + 1)^{a - 1} [(n a + 1) + (n a + 2) + \dots + (n a + n)]} = \frac{1}{60}

a =

a \in R

(the set of all real numbers),

a \neq - 1,

lim n \to \infty \frac{(1^{a} + 2^{a} + \dots + n^{a})}{{(n + 1)}^{a - 1} [(n a + 1) + (n a + 2) + \dots + (n a + n)]} = \frac{1}{60} .

a =

α ϵ R

(the set of all real numbers),

a \neq - 1

{lim}_{n \to \infty} \frac{(1^{a} + 2^{a} + \dots + n^{a})}{(n + 1)^{a - 1} [(n a + 1) + (n a + 2) + \dots + (n a + n)]} = \frac{1}{60}

α ϵ R

(the set of all real numbers),

a \neq - 1

{lim}_{n \to \infty} \frac{(1^{a} + 2^{a} + \dots + n^{a})}{(n + 1)^{a - 1} [(n a + 1) + (n a + 2) + \dots + (n a + n)]} = \frac{1}{60}

lim n \to \infty \frac{1^{a} + 2^{a} + . . . . . + n^{a}}{(n + 1)^{a - 1} [(n a + 1) + (n a + 2) + . . . . . + (n a + n)]} = \frac{1}{60}

for some positive real number

a, then a is equal to.

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