If y= 34+ 3 54 8+ 3 5 74 8 12+ … , then

Question

Accepted Answer

Correct answer: B. (b) We have, y= 34+ 3.54.8+ 3.5 .74.8 .12+ … y+1=1+ 34+ 3.54.8+ 3.5 .74.8 .12+ … =1+ ( -32 ) ( -12 )+ ( -32 )( -32-1) ( -12 )^22 !+ ( -32 )( -32-1)( -32-2) ( -12 )^33 !+ …=(1- 12)^-3/2= ( 12 )^-3/2=2^3/2=2 2y+1=2 2 ⇒ (y+1 )^2=8 ⇒y^2+2y+1=8 ⇒y^2+2y-7=0

$If y = \frac{3}{4} + \frac{3 \cdot 5}{4 \cdot 8} + \frac{3 \cdot 5 \cdot 7}{4 \cdot 8 \cdot 12} + \dots \infty, then$

Solution

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