Question

10. sum .45,015,.0005... upto infinity​

Answer 1

Answer:

One way to find the expansion of ( 1+ x ) ^(-2) is :

Let S = 1 - 2x + 3x^2 - ...

xS =. x - 2x^2 + ...

Adding both equations , we get

(1+x)S = 1 - x + x^2 - x^3

The RHS is an sum of an infinite GP with r = -x .

Sum of an infinite GP is given by : a/(1-r)

(1+x)S = 1/(1+x)

S = 1/(1+x)^2

Hence the binomial expansion of (1+x)^-2 is equal to S which is [ 1 - 2x + 3x ^2 ….. so on ]

Hope you get it…. Good Luck