Q8. Expand \frac{1}{(1+7x)^{1}} in ascending powers of x as far as the term in x^{2}
(A 1+21x+84x^{2}+\cdot\cdot\cdot(B)1\cdot\cdot\cdot21x-84x^{2}+
(C) 1+21x-84x^{2}+\cdot\cdot\cdot (
D) 1-21x+84x^{2}-\cdot\cdot\cdot
To expand the expression \frac{1}{(1+7x)^{1}} in ascending powers of x, we can use the binomial series. The formula for the binomial series expansion for a function f(x) = (1+x)^n is:
f(x) = 1 + nx + \frac{n(n-1)}{2!}x^2 + \frac{n(n-1)(n-2)}{3!}x^3 + ...
In this case, n = 1 and x = 7x. Plugging these values into the formula, we get:
\frac{1}{(1+7x)^{1}} = 1 + 1(7x) + \frac{1(1-1)}{2!}(7x)^2 + ...
Simplifying, we have:
\frac{1}{(1+7x)^{1}} = 1 + 7x + \frac{1}{2}(49x^2) + ...
Therefore, the correct answer is (A) 1+21x+84x^{2}+\cdot\cdot\cdot.