Can b 0 a 0 + b 1 a 1 + b 2 a 2...

gorgeousgen9487

gorgeousgen9487

Answered

2022-07-02

Can b 0 a 0 + b 1 a 1 + b 2 a 2 + b 3 a 3 + . . . + b n a n be represented as ...
Is this correct? (Last step After taking L.C.M.)
b 0 a 0 + b 1 a 1 + b 2 a 2 + b 3 a 3 + . . . + b n a n = k = 0 n ( b k a k ) = p = 0 n ( b p a p × q = 0 n a q ) q = 0 n a q
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Answer & Explanation

Brendan Bush

Brendan Bush

Expert

2022-07-03Added 14 answers

This is true simply by linearity of summation: if k is constant with respect to p then
p = 0 n k a p = k p = 0 n a p
Here, k = q = 0 n a q , which is constant with respect to p, so you can factor it out of the sum and cancel it.
You mention LCMs, though it doesn't look like you used them anywhere. In any case, your equation remains true if you replace q = 0 n a q by l c m { a q 1 q n }

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