Advertisements
Advertisements
प्रश्न
Using binomial theorem, indicate which of the following two number is larger: `(1.01)^(1000000)`, 10
Advertisements
उत्तर
`(1.01)^(1000000) = (1 + 0.01)^(1000000)`
= `""^(1000000)"C"_0(1)^(1000000) + ""^(1000000)"C"_1(1)^(999999)(0.01)^1 + ""^(1000000)"C"_2 (1)^(999998)(0.01)^2 + ""^(1000000)"C"_3(1)^(999997)(0.01)^3 + ..........`
= `1(1) + 1000000xx 1/10^2 + (1000000 xx 999999)/2 xx 1/10000 + .........`
= 1 + 10000 + 50 × 999999 + ........ which is > 10000
So `(1.01)^(1000000) > 10000`
(i.e.) `(1.01)^(1000000)` is larger
APPEARS IN
संबंधित प्रश्न
Evaluate the following using binomial theorem:
(101)4
Evaluate the following using binomial theorem:
(999)5
Expand the following by using binomial theorem.
(2a – 3b)4
Find the middle terms in the expansion of
`(3x + x^2/2)^8`
Sum of binomial coefficient in a particular expansion is 256, then number of terms in the expansion is:
Expand `(2x^2 - 3/x)^3`
Compute 994
Find the coefficient of x2 and the coefficient of x6 in `(x^2 -1/x^3)^6`
Find the coefficient of x4 in the expansion `(1 + x^3)^50 (x^2 + 1/x)^5`
If n is a positive integer, using Binomial theorem, show that, 9n+1 − 8n − 9 is always divisible by 64
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]
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
Prove that `"C"_0^2 + "C"_1^2 + "C"_2^2 + ... + "C"_"n"^2 = (2"n"!)/("n"!)^2`
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
