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Question

Question: The cube root of \(1 + 3x + 6x^{2} + 10x^{3} + .....\) is...

The cube root of 1+3x+6x2+10x3+.....1 + 3x + 6x^{2} + 10x^{3} + ..... is

A

1x+x2x3+.....1 - x + x^{2} - x^{3} + .....\infty

B

1+x3+x6+x9+......1 + x^{3} + x^{6} + x^{9} + ......

C

1+x+x2+x3+....1 + x + x^{2} + x^{3} + ....

D

None of these

Answer

1+x+x2+x3+....1 + x + x^{2} + x^{3} + ....

Explanation

Solution

We have (1+3x+6x2+10x3+.....)1/3(1 + 3x + 6x^{2} + 10x^{3} + .....)^{1/3}

= [(1x)3]1/3;[(1x)3=1+3x+6x2+...]\lbrack(1 - x)^{- 3}\rbrack^{1/3};\lbrack\because(1 - x)^{- 3} = 1 + 3x + 6x^{2} + ...\infty\rbrack

(1x)1=1+x+x2+...(1 - x)^{- 1} = 1 + x + x^{2} + ...\infty