Ltx→∞x+110+x+210+.......x+5010x10-1010=

Ltx→∞x+110+x+210+....x+5010x10−1010=Ltx→∞x101+1x10+1+2x10+....+1+50x10x101−10x10=1+1+....+11−0=50

Ltx→∞x+110+x+210+.......x+5010x10-1010=

Ltx→∞x+110+x+210+....x+5010x10−1010=Ltx→∞x101+1x10+1+2x10+....+1+50x10x101−10x10=1+1+....+11−0=50

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$\underset{x \to \infty}{L t} \frac{{(x + 1)}^{10} + {(x + 2)}^{10} + . . . . . . . {(x + 50)}^{10}}{x^{10} - 10^{10}} =$

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Detailed Solution

$\begin{array}{l} \underset{x \to \infty}{L t} \frac{{(x + 1)}^{10} + {(x + 2)}^{10} + .... {(x + 50)}^{10}}{x^{10} - 10^{10}} \\ = \underset{x \to \infty}{L t} x^{10} \frac{[{(1 + \frac{1}{x})}^{10} + {(1 + \frac{2}{x})}^{10} + .... + {(1 + \frac{50}{x})}^{10}]}{x^{10} (1 - {(\frac{10}{x})}^{10})} \\ = \frac{1 + 1 + .... + 1}{1 - 0} \\ = 50 \end{array}$