If y=3 x+6 x^ 2 +10 x^ 3 + , ∞, then (1)/(3) y- 1.4 3^ 2 2 y^ 2 + 1.4.7 3^ 2 3 y^ 3 - ∞ is equal to

Correct answer: A. x We have y=3 x+6 x^ 2 +10 x^ 3 + 1+y=1+3 x+6 x^ 2 +10 x^ 3 + 1+y=(1-x)^ -3 1-x=(1+y)^ -1 / 3 x=1-(1+y)^ -1 / 3 =(1)/(3) y- 1.4 3^ 2 · 2 y^ 2 + 1 · 4 · 7 3^ 2 · 3 y^ 3 -

BITSAT 2020

Exam: BITSAT
Year: 2020
Subject: Mathematics
Chapter: Sequences and Series

BITSAT 2020 · Mathematics · Sequences and Series

If y=3 x+6 x^ 2 +10 x^ 3 + , ∞, then (1)/(3) y- 1.4 3^ 2 2 y^ 2 +...

y=3 x+6 x^{2}+10 x^{3}+\ldots \ldots \ldots, \infty,

then

\frac{1}{3} y-\frac{1.4}{3^{2} 2} y^{2}+\frac{1.4.7}{3^{2} 3} y^{3}-\ldots \ldots \infty

is equal to

Options

A $x$
B $1-x$
C $1+x$
D $x^{x}$

Correct answer

A. $x$

Step-by-step solution

We have

y=3 x+6 x^{2}+10 x^{3}+\ldots \ldots\Rightarrow 1+y=1+3 x+6 x^{2}+10 x^{3}+\ldots\Rightarrow 1+y=(1-x)^{-3} \Rightarrow 1-x=(1+y)^{-1 / 3}\Rightarrow x=1-(1+y)^{-1 / 3}=\frac{1}{3} y-\frac{1.4}{3^{2} \cdot 2} y^{2}+\frac{1 \cdot 4 \cdot 7}{3^{2} \cdot 3} y^{3}-\ldots

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