How do you multiply summations?

Answer 1

Suppose we have 2 summations which we wish to multiply.

Summation 1: the sum of all odd numbers

1 + 3 + 5 + ... + (2k-1) = k*k

Summation 2: the sum of all even numbers

2 + 4 + 6 + ... + 2k = k * (k + 1)

We could multiply each term on the left side of the equal sign, one by one and make a sum:

1*2 + 3*4 + 5*6 + ... + (2k - 1) * 2k

OR We could mutiply the right sides of the equal sign

(K*K) * K * (k + 1) = __________simplify.