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
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 - 2/(3x))^9`
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`
Sum of the binomial coefficients is
Expand `(2x^2 - 3/x)^3`
Expand `(2x^2 -3sqrt(1 - x^2))^4 + (2x^2 + 3sqrt(1 - x^2))^4`
Compute 1024
Compute 994
Find the coefficient of x15 in `(x^2 + 1/x^3)^10`
Find the coefficient of x2 and the coefficient of x6 in `(x^2 -1/x^3)^6`
If n is an odd positive integer, prove that the coefficients of the middle terms in the expansion of (x + y)n are equal
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 the binomial coefficients of three consecutive terms in the expansion of (a + x)n are in the ratio 1 : 7 : 42, then find n
Choose the correct alternative:
The value of 2 + 4 + 6 + … + 2n is
