Advertisements
Advertisements
प्रश्न
State, by writing first four terms, the expansion of the following, where |b| < |a|
(a + b)−4
उत्तर
(a + b)−4
= `["a"(1 + "b"/"a")]^-4`
= `"a"^-4(1 + "b"/"a")^-4`
= `"a"^-4 [ 1 + (-4) "b"/"a" + ((-4)(-4 - 1))/(2!) ("b"/"a")^2 + ((-4)(-4 - 1)(-4 - 2))/(3!) ("b"/"a")^3 + ...]`
= `"a"^-4 [1 - (4"b")/"a" + ((-4)(-5))/2 * "b"^2/"a"^2 + ((-4)(-5)(-6))/6 * "b"^3/"a"^3 + ...]`
= `"a"^-4 [1 - (4"b")/"a" + (10"b"^2)/"a"^2 - (20"b"^3)/"a"^3 + ...]`
APPEARS IN
संबंधित प्रश्न
State, by writing first four terms, the expansion of the following, where |x| < 1
(1 + x)−4
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")^(1/4)`
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")^(-1/3)`
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
`(2 - 3x)^(1/3)`
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
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
Answer the following:
Find approximate value of `1/4.08` upto four places of decimals
