# How can I write the given statement using mathematical symbols

How do I write this in mathematical symbols: "Result is equal to the sum of product of $a(i)$ and $b(j)$ when $i,j$ are natural numbers and satisfy the property $i+j = k$"?

I forgot to add one more constraint that :

i and j are in the range [0,n] k is in the range [0,2n]

n is a natural number.

Sorry for the late update.

• $\sum\limits_{i+j=k} a_i b_j$ – Mher Oct 7 '14 at 14:01

You can note that $j=k-i$ and say $$c(k)=\sum _{i=0}^{k}a(i)b(k-i)$$
• You can change the indices to reflect that $i=0, j=0$ are allowed as I have done above. If $a(i),b(j)$ are defined to be zero outside the range $[0,n]$ you don't have to do more. If you want, you can put $i, k-i \le n$ below the sum sign to emphasize it. – Ross Millikan Oct 8 '14 at 13:15