Advertisements
Advertisements
Question
Simplify first three terms in the expansion of the following
`(5 + 4x)^(-1/2)`
Solution
`(5 + 4x)^(-1/2)`
= `[5(1 + 4/5x)]^(-1/2)`
= `5^(-1/2) (1 + (4x)/5)^(-1/2)`
= `5^(-1/2)[1 + (-1/2)((4x)/5) + ((-1/2)(-1/2 - 1))/(2!) ((4x)/5)^2 + ....]`
= `5^(-1/2)[1 - (2x)/5 + ((-1/2)(-3/2))/2 ((16x^2)/25) + ....]`
= `5^(-1/2) [ 1 - (2x)/5 + (6x^2)/25 + ......]`
APPEARS IN
RELATED QUESTIONS
State, by writing first four terms, the expansion of the following, where |x| < 1
`(1 - x)^(1/3)`
State, by writing first four terms, the expansion of the following, where |x| < 1
(1 – x2)–3
State, by writing first four terms, the expansion of the following, where |x| < 1
(1 + x2)–1
State, by writing first four terms, the expansion of the following, where |b| < |a|
(a − b)−3
State, by writing first four terms, the expansion of the following, where |b| < |a|
(a + b)−4
State, by writing first four terms, the expansion of the following, where |b| < |a|
`("a" + "b")^(1/4)`
State, by writing first four terms, the expansion of the following, where |b| < |a|
`("a" - "b")^(-1/4)`
Simplify first three terms in the expansion of the following
(1 + 2x)–4
Simplify first three terms in the expansion of the following
`(1 + 3x)^(-1/2)`
Simplify first three terms in the expansion of the following
`(5 - 3x)^(-1/3)`
Use binomial theorem to evaluate the following upto four places of decimal
`sqrt(99)`
Use binomial theorem to evaluate the following upto four places of decimal
`root(3)(126)`
Use binomial theorem to evaluate the following upto four places of decimal
`root(4)(16.08)`
Use binomial theorem to evaluate the following upto four places of decimal
(1.02)–5
Use binomial theorem to evaluate the following upto four places of decimal
(0.98)–3
Show That C1 + C2 + C3 + .... Cn = 2n − 1
Show That C0 + 2C1 + 3C2 + 4C3 + ... + (n + 1)Cn = (n + 2)2n−1
Answer the following:
Expand `((2x)/3 - 3/(2x))^4`
Answer the following:
Using binomial theorem, find the value of `root(3)(995)` upto four places of decimals
