Show that pa1-1-pqa2-1-a3-1-pqa4- pa1-1-qa2-1-pa3-1-qa4-

We can write p( a _ 1 + a pq a _ 3 + 1 R _ 2 #160; #160; ) =p a _ 1 + a pq a _ 2 + 1 R _ 2 #160; =p a _ 1 + 1 q a _ 2 + 1 p R _ 2 #160; ...

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Byju's Answer

Standard XII

Physics

Energy of a Capacitor

Show that p...

Question

Show that $p (a_{1} + \frac{1}{p q a_{2} +} \frac{1}{a_{3} +} \frac{1}{p q a_{4} +} . . . .) = p a_{1} + \frac{1}{q a_{2} +} \frac{1}{p a_{3} +} \frac{1}{q a_{4} +} . . . . .$ .

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Solution

We can write $p ⎛ ⎜ ⎜ ⎜ ⎝ a_{1} + \frac{a}{p q a_{3} + \frac{1}{R_{2}}} ⎞ ⎟ ⎟ ⎟ ⎠ = p a_{1} + \frac{a}{p q a_{2} + \frac{1}{R_{2}}} = p a_{1} + \frac{1}{q a_{2} + \frac{1}{p R_{2}}}$
Where, $R_{2} = a_{3} + \frac{1}{p q a_{4}} . . . .$
Similarly,
$p R_{2} = p ⎛ ⎜ ⎜ ⎜ ⎝ a_{3} + \frac{1}{p q a_{4} + \frac{1}{R_{4}}} ⎞ ⎟ ⎟ ⎟ ⎠ = p a_{3} + \frac{1}{q a_{4} + \frac{1}{p R_{4}}}$
and so on..
Therefore, $p (a_{1} + \frac{1}{p q a_{2}} \frac{1}{a_{3} +} \frac{1}{p q a_{4} +} . . . .)$
$= p a_{1} + \frac{1}{q a_{2} +} \frac{1}{p a_{3}} \frac{1}{q a_{4} +} . . . . .$

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Show that p(a1+1pqa2+1a3+1pqa4+....)=pa1+1qa2+1pa3+1qa4+......

We can write p⎛⎜ ⎜ ⎜⎝a1+apqa3+1R2⎞⎟ ⎟ ⎟⎠=pa1+apqa2+1R2=pa1+1qa2+1pR2Where, R2=a3+1pqa4....Similarly,pR2=p⎛⎜ ⎜ ⎜⎝a3+1pqa4+1R4⎞⎟ ⎟ ⎟⎠=pa3+1qa4+1pR4and so on..Therefore, p(a1+1pqa21a3+1pqa4+....)=pa1+1qa2+1pa31qa4+.....

Show that $p (a_{1} + \frac{1}{p q a_{2} +} \frac{1}{a_{3} +} \frac{1}{p q a_{4} +} . . . .) = p a_{1} + \frac{1}{q a_{2} +} \frac{1}{p a_{3} +} \frac{1}{q a_{4} +} . . . . .$ .