| |
|
|
| |
 |
| Some Applications of Binomial Theorem for Fractional Index |
|
 If x be numerically so small that its cube and higher powers may be  x3, x4, x5, …. are all approximately zero. |
| |
 If x be numerically so small that its square and higher powers may be neglected, then (1+x)n= 1+nx (approximately), because x2, x3, x4,…. are all approximately zero. |
| |
| Example: |
| |
| If x be numerically so small that its cube and higher powers may be neglected, then find the binomial expansions for: |
| |
| i) (1 + 2x)-4 |
| |
 |
| |
| Suggested answer: |
| |
| i) (1 + 2x)-4 |
| |
 |
| |
  |
| |
 |
| |
 |
| |
 |
| |
 |
| |
 |
| |
 |
| |
|
|
| |
|
|
| |
|
|
|
