Question
Question: The cube root of \(1 + 3x + 6x^{2} + 10x^{3} + .....\) is...
The cube root of 1+3x+6x2+10x3+..... is
A
1−x+x2−x3+.....∞
B
1+x3+x6+x9+......
C
1+x+x2+x3+....
D
None of these
Answer
1+x+x2+x3+....
Explanation
Solution
We have (1+3x+6x2+10x3+.....)1/3
= [(1−x)−3]1/3;[∵(1−x)−3=1+3x+6x2+...∞]
⇒ (1−x)−1=1+x+x2+...∞