Question

How do you find the sum of the series `3i` from i=1 to i=6?

Answer 1

The sum of the series is 63.

Explanation:

Use the summation property `sum_i ^n ca_i = csum_i ^n a_i`, where c is a constant.

`sum_1 ^6 3i=3*sum_1 ^6 i`

Use the summation property `sum_(x=1) ^n x = frac{n(n+1)}[2}`

`3* sum_1 ^6 i= 3 *frac{6(6+1)}{2} = 63`

Alternatively, you could substitute i =1, i=2, i=3,...i=6 into 3i and then add.

`3(1) +3(2)+3(3)+3(4)+3(5)+3(6) = 63`