Advertisements
Advertisements
Question
Compute 994
Solution
994 = (100 – 1)4
= 4C0 (100)4(1)0 + 4C1 (100)4–1 (– 1)1 + 4C2 (100)4–2 (– 1)2 + 4C3 (100)4–3 (– 1)3 + 4C4 (100)4–4 (– 1)4
= `1 xx 100^4 xx 1 - 4 xx 100^3 xx 1 + (4 xx 3)/(1 xx 2) xx 100^2 xx 1 - 4 xx 100^1 xx 1 + 1 xx 1 xx 1`
= 100000000 – 4 × 1000000 + 6 × 10000 – 400 + 1
= 100000000 – 4000000 + 60000 -400+1
= 96059601
APPEARS IN
RELATED QUESTIONS
Evaluate the following using binomial theorem:
(101)4
Expand the following by using binomial theorem.
(2a – 3b)4
Expand the following by using binomial theorem.
`(x + 1/y)^7`
Find the middle terms in the expansion of
`(x + 1/x)^11`
Find the term independent of x in the expansion of
`(x^2 - 2/(3x))^9`
Find the term independent of x in the expansion of
`(x - 2/x^2)^15`
Prove that the term independent of x in the expansion of `(x + 1/x)^(2n)` is `(1*3*5...(2n - 1)2^n)/(n!)`.
Show that the middle term in the expansion of is (1 + x)2n is `(1*3*5...(2n - 1)2^nx^n)/(n!)`
The middle term in the expansion of `(x + 1/x)^10` is
The constant term in the expansion of `(x + 2/x)^6` is
The last term in the expansion of (3 + √2 )8 is:
Compute 97
Using binomial theorem, indicate which of the following two number is larger: `(1.01)^(1000000)`, 10
Find the coefficient of x4 in the expansion `(1 + x^3)^50 (x^2 + 1/x)^5`
If n is a positive integer and r is a non-negative integer, prove that the coefficients of xr and xn−r in the expansion of (1 + x)n are equal
In the binomial expansion of (a + b)n, if the coefficients of the 4th and 13th terms are equal then, find n
If the binomial coefficients of three consecutive terms in the expansion of (a + x)n are in the ratio 1 : 7 : 42, then find n
In the binomial expansion of (1 + x)n, the coefficients of the 5th, 6th and 7th terms are in AP. Find all values of n
Choose the correct alternative:
The remainder when 3815 is divided by 13 is
