Let n be an integer greater than 1 and let an - 1 logn1001 if b - a3 - a4 - a5 - a6 and c - a11 - a12 - a13 - a14 - a15- Then value of b - c is equal to

a_n =1log_n 1001 log_xP=log_y Plog_y x b=a_3+a_4+a_5+a_6 =1log_3 1001+1log_4 1001+1log_5 1001+1log_6 1001 =log_2 3log_2 1001+log_2 4log ...

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Continuity in an Interval

Let n be an i...

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Let n be an integer greater than 1 and let $a_{n} = \frac{1}{{log}_{n} 1001}$ if $b = a_{3} + a_{4} + a_{5} + a_{6}$ and $c = a_{11} + a_{12} + a_{13} + a_{14} + a_{15}$ . Then value of $(b - c)$ is equal to

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A_{1} = [a_{1}] A_{2} = [\begin{matrix} a_{2} & a_{3} a_{4} & a_{5} \end{matrix}] A_{3} = ⎡ ⎢ ⎣ \begin{matrix} a_{6} & a_{7} & a_{8} a_{9} & a_{10} & a_{11} a_{12} & a_{13} & a_{14} \end{matrix} ⎤ ⎥ ⎦ \dots \dots A_{n} = [\dots] where a_{r} = [{log}_{2} r]

([\cdot]

)

A_{10}

a_{n} = \int_{0}^{\frac{π}{4}} {tan}^{n} x d x .

a_{2} + a_{4}, a_{3} + a_{5}, a_{4} + a_{6}

a_{n} = \int_{0}^{π / 4} t a n^{n} x d x

a_{2} + a_{4}, a_{3} + a_{5}, a_{4} + a_{6}

a_{1}, a_{2}, a_{3}, \dots, a_{15}

a_{1} + a_{2} + \dots + a_{10} = A

a_{6} + a_{7} + \dots + a_{15} = B

B - A = 200

B + A = 860,

a_{15}

⎡ ⎢ ⎣ \begin{matrix} cos θ - sin θ 0 \end{matrix} \begin{matrix} sin θ cos θ 0 \end{matrix} \begin{matrix} 001 \end{matrix} ⎤ ⎥ ⎦

a_{11} A_{11} + a_{12} A_{12} + a_{13} A_{13} =

A_{11}, A_{12} A_{13}

a_{11}, a_{12}, a_{13}

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