# 700 Followers Problem!

Algebra Level 4

Expanding $$(1+0.2)^{1000}$$ by the Binomial theorem gives

$${1000 \choose 0}(0.2)^0+{1000 \choose 1}(0.2)^1+{1000 \choose 2}(0.2)^2+\cdots+{1000 \choose 1000}(0.2)^{1000}$$ $$= A_0 + A_1 + A_2 + \cdots + A_{1000}$$

Where $$A_k = {1000 \choose k}(0.2)^k$$ for $$k = 0,1,2,\ldots,1000$$.

For which $$k_{}^{}$$ is $$A_k^{}$$ the largest?

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