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I've just started with Mathematica and I'm still learning the basics.

At the moment I want Mathematica to display series multiplication in this form, so I can investigate generating functions better. $c(x)$ is an infinite series, but I just want to look at a few terms in the multiplication.

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How do I do it? I got to here but couldn't get it to expand.

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(copyable plaintext version)

Sum[Subscript[c, i] x^i, {i, 0, ∞}] //TeXForm

$\sum _{i=0}^{\infty } c_i x^i$

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Truncate your sum, and use Series:

s = Sum[Subscript[c, i] x^i, {i, 0, 10}];
Series[s^2, {x, 0, 10}] //TeXForm

$c_0^2+2 c_0 c_1 x+\left(c_1^2+2 c_0 c_2\right) x^2+\left(2 c_1 c_2+2 c_0 c_3\right) x^3+\left(c_2^2+2 c_1 c_3+2 c_0 c_4\right) x^4+\left(2 c_2 c_3+2 c_1 c_4+2 c_0 c_5\right) x^5+\left(c_3^2+2 c_2 c_4+2 c_1 c_5+2 c_0 c_6\right) x^6+\left(2 c_3 c_4+2 c_2 c_5+2 c_1 c_6+2 c_0 c_7\right) x^7+\left(c_4^2+2 c_3 c_5+2 c_2 c_6+2 c_1 c_7+2 c_0 c_8\right) x^8+\left(2 c_4 c_5+2 c_3 c_6+2 c_2 c_7+2 c_1 c_8+2 c_0 c_9\right) x^9+\left(c_5^2+2 c_4 c_6+2 c_3 c_7+2 c_2 c_8+2 c_1 c_9+2 c_0 c_{10}\right) x^{10}+O\left(x^{11}\right)$

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