Question

The sequence of numbers u1 U2 u3 u n satisfies the relation un is equal to u n+ 1/2 ^ n - 1 for n is greater than 1 if n>1.If U1= 1 find the values of U3 and U4

Answer 1

To find the values of U3 and U4, we need to use the given relation and the initial value U1=1.

Using the given relation, we can find the value of U2:
U2 = U1 + 1/2^(1-1) = U1 + 1/2^0 = U1 + 1/1 = U1 + 1 = 1 + 1 = 2

Using the given relation again, we can find the value of U3:
U3 = U2 + 1/2^(2-1) = U2 + 1/2^1 = U2 + 1/2 = 2 + 1/2 = 2.5

Using the given relation once more, we can find the value of U4:
U4 = U3 + 1/2^(3-1) = U3 + 1/2^2 = U3 + 1/4 = 2.5 + 1/4 = 2.75

Therefore, the values of U3 and U4 are 2.5 and 2.75, respectively.