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Byju's Answer

Standard XII

Mathematics

nth Term of A.P

Let a n ,nϵ...

Question

Let $a_{n}, n ϵ N$ is an A.P. with common difference 'd' and all whose terms are non-zero. If n approaches infinity, then the sum $\frac{1}{a_{1} a_{2}} + \frac{1}{a_{2} a_{3}} + . . . + \frac{1}{a_{n} a_{n + 1}}$ will approach

\frac{1}{a_{1} d}

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\frac{2}{a_{1} d}

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\frac{1}{2 a_{1} d}

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a_{1} d

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Solution

The correct option is C $\frac{1}{a_{1} d}$
$\frac{1}{a_{1} a_{2}} + \frac{1}{a_{2} a_{3}} + . . .$
$= \frac{1}{d} (\frac{a_{2} - a_{1}}{a_{1} a_{2}} + \frac{a_{3} - a_{2}}{a_{2} a_{3}} + . . .)$
$= \frac{1}{d} (\frac{1}{a_{1}} - \frac{1}{a_{2}} + \frac{1}{a_{2}} - \frac{1}{a_{3}} + . . .)$
$= \frac{1}{a_{1} d}$

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Let an,nϵN is an A.P. with common difference 'd' and all whose terms are non-zero. If n approaches infinity, then the sum 1a1a2+1a2a3+...+1anan+1 will approach

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