Can't understand the Notation of SUM!
sorry to do this but Im in a hurry so im just giving this file..
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Re: Can't understand the Notation of SUM!
The first two just means that you sum for all values $k=1$ to $n$ .
For example,
$\sum\limits_{k=1}^4 (k^2) = 1^2 + 2^2 + 3^2 + 4^2$
$\sum\limits_{k=0}^5 (3^k) = 3^0 + 3^1 + 3^2 + 3^3 + 3^4 + 3^5$
$\sum\limits_{k=5}^6 (x^2+kx +k^x +x^k) = (x^2+5x +5^x +x^5) + (x^2+6x +6^x +x^6)$
$\sum\limits_{i=-2}^{n^2} (e^i) = e^{-2} + e^{-1} + e^0 + e^1 + e^2 + e^3 + \cdot + e^{n^2-1} + e^{n^2}$
For example,
$\sum\limits_{k=1}^4 (k^2) = 1^2 + 2^2 + 3^2 + 4^2$
$\sum\limits_{k=0}^5 (3^k) = 3^0 + 3^1 + 3^2 + 3^3 + 3^4 + 3^5$
$\sum\limits_{k=5}^6 (x^2+kx +k^x +x^k) = (x^2+5x +5^x +x^5) + (x^2+6x +6^x +x^6)$
$\sum\limits_{i=-2}^{n^2} (e^i) = e^{-2} + e^{-1} + e^0 + e^1 + e^2 + e^3 + \cdot + e^{n^2-1} + e^{n^2}$
Re: Can't understand the Notation of SUM!
The last one means that you sum over all $i,j$ such that they satisfy the conditions written below the summation sign. For example,
$\sum\limits_{\substack{0 \leq i+j \leq 2 \\ 0 \leq j <2 \\ 0\leq i}} x^iy^j = x^0y^0 + x^0y^1 + x^1y^0 + x^1y^1 + x^2y^0$
$\sum\limits_{\substack{i+j = 3 \\ i >1 \\ j \geq -1}} i^j = 2^1 + 3^0 + 4^{-1}$
$\sum\limits_{\substack{0 \leq i+j \leq 2 \\ 0 \leq j <2 \\ 0\leq i}} x^iy^j = x^0y^0 + x^0y^1 + x^1y^0 + x^1y^1 + x^2y^0$
$\sum\limits_{\substack{i+j = 3 \\ i >1 \\ j \geq -1}} i^j = 2^1 + 3^0 + 4^{-1}$
Re: Can't understand the Notation of SUM!
Was I able to make it clear?