K -lim x - k -110 N x - k m - x m -101000 is m -101A- 102B- 103C- 104D- 10

The correct option is B 103 Divide above and below by x^m, then k = lim_x→∞ ( ∑_k=1^1000(1+k/x)^m/1+10^1000/x^m ) = 1+1+1+...upto 1000 times/1+0 = 1000 = 10^3 ...

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Standard XI

Mathematics

Numerically Greatest Term

k =lim x →∞∑ ...

Question

k = $lim x \to \infty ⎛ ⎜ ⎜ ⎝ \frac{1000 \sum k = 1 (x + k)^{m}}{x^{m} + 10^{1000}} ⎞ ⎟ ⎟ ⎠$ is (m > 101)

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Solution

The correct option is C
10³

Divide above and below by $x^{m}$ , then

k = $lim x \to \infty ⎛ ⎜ ⎜ ⎝ \frac{1000 \sum k = 1 (1 + \frac{k}{x})^{m}}{1 + \frac{10^{1000}}{x^{m}}} ⎞ ⎟ ⎟ ⎠$

= $\frac{1 + 1 + 1 + . . . u p t o 1000 t i m e s}{1 + 0}$

= 1000 = $10^{3}$

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k = limx→∞⎛⎜ ⎜⎝1000∑k=1(x+k)mxm+101000⎞⎟ ⎟⎠ is (m > 101)

The correct option is C 103 Divide above and below by xm, then k = limx→∞⎛⎜ ⎜⎝1000∑k=1(1+kx)m1+101000xm⎞⎟ ⎟⎠ = 1+1+1+...upto 1000 times1+0 = 1000 = 103

k = $lim x \to \infty ⎛ ⎜ ⎜ ⎝ \frac{1000 \sum k = 1 (x + k)^{m}}{x^{m} + 10^{1000}} ⎞ ⎟ ⎟ ⎠$ is (m > 101)

The correct option is C
10³

Divide above and below by $x^{m}$ , then

k = $lim x \to \infty ⎛ ⎜ ⎜ ⎝ \frac{1000 \sum k = 1 (1 + \frac{k}{x})^{m}}{1 + \frac{10^{1000}}{x^{m}}} ⎞ ⎟ ⎟ ⎠$

= $\frac{1 + 1 + 1 + . . . u p t o 1000 t i m e s}{1 + 0}$

= 1000 = $10^{3}$