If the sum of 1-4x-7 x 2 -10 x 3 - - x - -1 is 35 16 then x-

The correct option is C 1 5 ...

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Ratio and Proportion

If the sum of...

Question

If the sum of $1 + 4 x + 7 x^{2} + 10 x^{3} + . . . . \infty (| x | < 1)$ is $\frac{35}{16}$ then $x =$

\frac{1}{3}

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\frac{1}{4}

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\frac{1}{5}

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\frac{1}{6}

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1 + 4 x + 7 x^{2} + 10 x^{3} + . . .

\frac{35}{16}

x

| x | < 1

1 + 4 x + 7 x^{2} + 10 x^{3} + \dots

\frac{35}{16}

x =

1 + 2 x + 3 x^{2} + 4 x^{3} + . . . ., | x | < 1

1 + 4 x + 7 x^{2} + 10 x^{3} + . . . ., | x | < 1

2 \times 1 + 3 \times 2 + 4 \times 4 + 5 \times 8 + . . . .

i n f i n i t e

1 + 4 x + 7 x^{2} + 10 x^{3} + . . ., | x | < 1

(x + 1 | = 4 x + 1 = 4 or x + 1 = - 4 x = 3 or x = - 5

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