Question

Write the four terms of the binomial expansion (2-1/x)^5 in ascending powers of X. Hence find (1.9)^5
Must be too hard for the AI to handle ....

(2-1/x)^5
= 2^5 + 5(2^4)(-1/x) + 10(2^3)(-1/x)^2 + 10(2^2)(-1/x)^3 + ..
= 32 - 80/x + 80/x^2 - 40/x^3 + ...

in (1.9)^5, we would have (2 - .1)^5 , -1/x = -.1, 1/x = 1/10, x = 10
so
(1.9^5) = 32 - 80/10 + 80/100 - 40/1000
= 32 - 8 + .8 - .04 +
= 24.76

actual value of 1.9^5 using calculator = 24.76099...
looks like your expansion is in decreasing powers of x -- that is, increasing powers of 1/x
One expansion is
1 - ∑ (1-x)^n

Related Questions

find the first 3 terms in the expansion of (x+4)(1+3x)^-2 as a series in ascending powers. I expa... in the binomial expansion of (1+x/k)^n, where k is a constant and n is a positive integer, the coeff... Find 1.The first 4 terms of the binomial expansion in ascending powers of x of (1+x/4)^8. 2.Use y... write down the first four terms of the binomial expansion of (1-y)^8 in ascending power of y.By putt...