The value of limx- x-110-x-210-x-20010x10-20010 is

Limx→∞ nbsp;x+110+x+210+......+x+20010x10+20010=limx→∞ nbsp;x+110+x+210+......+x+20010x10x10+20010x10=limx→∞ nbsp;1+1x10+1+2x10+......+1+200x101+200x10=1+ ...

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Byju's Answer

Standard XII

Mathematics

Substitution Method to Remove Indeterminate Form

The value of ...

Question

The value of $lim x \to \infty \frac{{(x + 1)}^{10} + {(x + 2)}^{10} + . . . . . . + {(x + 200)}^{10}}{x^{10} + 200^{10}}$ is

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Solution

$lim x \to \infty \frac{{(x + 1)}^{10} + {(x + 2)}^{10} + . . . . . . + {(x + 200)}^{10}}{x^{10} + 200^{10}} = lim x \to \infty \frac{\frac{{(x + 1)}^{10} + {(x + 2)}^{10} + . . . . . . + {(x + 200)}^{10}}{x^{10}}}{\frac{x^{10} + 200^{10}}{x^{10}}} = lim x \to \infty \frac{{(1 + \frac{1}{x})}^{10} + {(1 + \frac{2}{x})}^{10} + . . . . . . + {(1 + \frac{200}{x})}^{10}}{1 + {(\frac{200}{x})}^{10}} = \frac{{(1 + 0)}^{10} + {(1 + 0)}^{10} + . . . . . . + {(1 + 0)}^{10}}{1 + {(0)}^{10}} = \frac{1 + 1 + . . . . + 1 (200 times)}{1 + 0} = 200$

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Similar questions

lim x \to \infty \frac{{(x + 1)}^{10} + {(x + 2)}^{10} + . . . . + {(x + 100)}^{10}}{x^{10} + 10^{10}}

Q. The value of

\lim_{x \to \infty} \frac{{(x + 1)}^{10} + {(x + 2)}^{10} + . . . + {(x + 100)}^{10}}{x^{10} + 10^{10}}

is

(a) 10

(b) 100

(c) 10¹⁰

(d) none of these

The value of ${lim}_{x \to \infty} \frac{(x + 1)^{10} + (x + 2)^{10} + \dots + (x + 100)^{10}}{x^{10} + 10^{10}}$ is

lim x \to \infty \frac{{(x + 1)}^{10} + {(x + 2)}^{10} + . . . . {(x + 100)}^{10}}{x^{10} + 10^{10}}

Q. Evaluate:

lim x \to \infty \frac{(x + 1)^{10} + (x + 2)^{10} + \dots . . + (x + 100)^{10}}{x^{10} + 10^{10}}

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The value of limx→∞ (x+1)10+(x+2)10+......+(x+200)10x10+20010 is

limx→∞ (x+1)10+(x+2)10+......+(x+200)10x10+20010=limx→∞ (x+1)10+(x+2)10+......+(x+200)10x10x10+20010x10=limx→∞ (1+1x)10+(1+2x)10+......+(1+200x)101+(200x)10=(1+0)10+(1+0)10+......+(1+0)101+(0)10=1+1+....+1 (200 times)1+0=200

The value of $lim x \to \infty \frac{{(x + 1)}^{10} + {(x + 2)}^{10} + . . . . . . + {(x + 200)}^{10}}{x^{10} + 200^{10}}$ is