Is (1/a^2 + 1/a^4 + 1/a^6 +...) > (1/a + 1/a^3 + 1/a^5 +...)? A. 0< a \leq 1 B. One of the roots of the equation 4x^2-4x+1 = 0 is a

Question 71

Is $$(1/a^2 + 1/a^4 + 1/a^6 +...) > (1/a + 1/a^3 + 1/a^5 +...)$$?
A. $$0< a \leq 1$$
B. One of the roots of the equation $$4x^2-4x+1 = 0$$ is a

Solution

Consider the first statement:
When the common ratio is less than 1 we can apply the formula of sum of infinite terms.
So, LHS = $$1/(a^2 - 1)$$
RHS = $$a/(a^2 - 1)$$
If a<1 then LHS<RHS

If a = 1,then LHS = RHS

So, we cannot answer the question using statement 1 alone

Using statement 2 alone, we know that a = 1/2. So, RHS > LHS
Hence, option a)

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Is $$(1/a^2 + 1/a^4 + 1/a^6 +...) > (1/a + 1/a^3 + 1/a^5 +...)$$?A. $$0< a \leq 1$$B. One of the roots of the equation $$4x^2-4x+1 = 0$$ is a

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Is $$(1/a^2 + 1/a^4 + 1/a^6 +...) > (1/a + 1/a^3 + 1/a^5 +...)$$?
A. $$0< a \leq 1$$
B. One of the roots of the equation $$4x^2-4x+1 = 0$$ is a