Advertisements
Advertisements
Question
Compute 994
Advertisements
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
Evaluate the following using binomial theorem:
(999)5
Expand the following by using binomial theorem.
`(x + 1/y)^7`
Find the 5th term in the expansion of (x – 2y)13.
The last term in the expansion of (3 + √2 )8 is:
Sum of binomial coefficient in a particular expansion is 256, then number of terms in the expansion is:
Sum of the binomial coefficients is
Expand `(2x^2 -3sqrt(1 - x^2))^4 + (2x^2 + 3sqrt(1 - x^2))^4`
Compute 1024
Using binomial theorem, indicate which of the following two number is larger: `(1.01)^(1000000)`, 10
Find the coefficient of x15 in `(x^2 + 1/x^3)^10`
Find the coefficient of x4 in the expansion `(1 + x^3)^50 (x^2 + 1/x)^5`
Find the constant term of `(2x^3 - 1/(3x^2))^5`
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 value of 2 + 4 + 6 + … + 2n is
Choose the correct alternative:
The remainder when 3815 is divided by 13 is
