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STD 11 - 12. limits — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 12. limits4 Marks
MCQ
$\mathop {\lim }\limits_{x \to 1} \frac{{x + {x^2} + ...... + {x^n} - n}}{{x - 1}}$ is equal to
  • A
    $n$
  • B
    $\frac{{n + 1}}{2}$
  • ✓
    $\frac{{n\left( {n + 1} \right)}}{2}$
  • D
    $\frac{{n\left( {n - 1} \right)}}{2}$
✓

Answer

Correct option: C.
$\frac{{n\left( {n + 1} \right)}}{2}$
c
$\mathop {\lim }\limits_{x \to 1} \left\{ {\frac{{x - 1}}{{x - 1}} + \frac{{{x^2} - 1}}{{x - 1}} +  \ldots  \ldots  + \frac{{{x^n} - 1}}{{x - 1}}} \right\}$

$ = 1 + 2 + ....n = \frac{{n\left( {n + 1} \right)}}{2}$

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