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
Expand the following by using binomial theorem.
`(x + 1/y)^7`
Expand the following by using binomial theorem.
`(x + 1/x^2)^6`
Find the middle terms in the expansion of
`(x + 1/x)^11`
Find the term independent of x in the expansion of
`(x - 2/x^2)^15`
Find the term independent of x in the expansion of
`(2x^2 + 1/x)^12`
Find the Co-efficient of x11 in the expansion of `(x + 2/x^2)^17`
The constant term in the expansion of `(x + 2/x)^6` is
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 - 3/x)^3`
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`
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
If a and b are distinct integers, prove that a − b is a factor of an − bn, whenever n is a positive integer. [Hint: write an = (a − b + b)n and expaand]
