Applications of Binomial Theorem

• 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:

Suggested answer:

i) (1 + 2x)^-4