Let the rth term Tr of a series is given by Tr-r1-r2-r4- then limn-r-1nTr equals-

The correct option is A 12 As T_ r = r 1+r^ 2 +r^ 4 = 1 2 2r 1+r^ 2 +r^ 4 = 1 2 ( 1 r ^ 2 r+1 1 r ^ 2 +r+1 nbsp;) = 1 2 ...

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Let the rth...

Question

Let the $r^{t h}$ term $T_{r}$ of a series is given by $T_{r} = \frac{r}{1 + r^{2} + r^{4}}$ , then ${lim}_{n \to \infty} n \sum r = 1 T_{r}$ equals?

1

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\frac{1}{4}

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\frac{1}{2}

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none of these

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r t h

t_{r}

t_{r} = \frac{r}{1 + r^{2} + r^{4}}

lim n \to \infty n \sum r = 1 t_{r}

t_{r}

t_{r} = \frac{r}{1 + r^{2} + r^{4}}

{lim}_{n \to \infty} \sum_{r = 1}^{n} t_{r}

r^{t h}

T_{r} = \frac{r}{1 - 3 r^{2} + r^{4}} .

lim n \to \infty \sum_{r = 1}^{n} T_{r}

r^{th}

T_{r} = \frac{r}{1 - 3 r^{2} + r^{4}} .

- 2 \infty \sum r = 1 T_{r}

t_{r} = \frac{r}{1 + r^{2} + r^{4}}

{lim}_{n \to \infty} \sum_{r = 1}^{n} t_{r}

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