The value of -1 - 2008 -1 - 2009 -1 - 2010 -1 - 2011-2013 is -

The correct option is A 2009 √(1+2008√(1+2009√(1+2010√(1+2011.2013)))) Or nbsp; √(1+2008√(1+2009√(1+2010.2012))) ⇒√(1+2008√(1+2009.2011)) ⇒ ...

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Expansion of (a ± b ± c)²

The value of ...

Question

The value of $\sqrt{1 + 2008 \sqrt{1 + 2009 \sqrt{1 + 2010 \sqrt{1 + 2011.2013}}}}$ is .............

2009

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2010

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2011

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2013

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Solution

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1 \times 2009 + 2 \times 2008 + 3 \times 2007 + . . . . . . + 2009 \times 1 = 2009 \times 2011 x

x

x \neq 0, \pm 1,

\frac{\frac{1}{_{x} 2007} - \frac{1}{_{x} 2009}}{\frac{1}{_{x} 2008} - \frac{1}{_{x} 2010}}

(3 + x^{2008} + x^{2009})^{2010} = a_{0} + a_{1} x + a_{2} x^{2} + \dots + a_{n} x^{n}

a_{0} - \frac{1}{2} a_{1} - \frac{1}{2} a_{2} + a_{3} - \frac{1}{2} a_{4} - \frac{1}{2} a_{5} + a_{6} - \dots

n

S

x

(x^{2010} + 1) (1 + x^{2} + x^{4} + \dots + x^{2008}) = 2010 x^{2009}

S

(3 + x^{2008} + x^{2009})^{2010} = a_{0} + a_{1} x + a_{2} x^{2} + \dots + a_{n} x^{n}

a_{0} - \frac{1}{2} a_{1} - \frac{1}{2} a_{2} + a_{3} - \frac{1}{2} a_{4} - \frac{1}{2} a_{5} + a_{6} - \dots

n

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