Question

Write the series using summation notation. Then find the sum of the series.

1 + 2 + 3 + ++ + 12

And

1/2 + 1/4 + 1/6 + ++ + 1/14

Answer 1

Hello, please consider the following.

`\displaystyle 1+2+3+...+12=\sum_(k=1)^(k=12) {k}=(12*13)/(2)=6*13=78`

For the second we will need to put on the same denominator.

`\displaystyle (1)/(2)+(1)/(4)+...+(1)/(14)=\sum_(k=1)^(k=7) {(1)/(2k)}\\\\=(1)/(2)(420+210+140+105+84+70+60)/(5*7*3*2*2)\\\\=(1)/(2)(1089)/(420)\\\\=(1089)/(840)=1.296429...`

Thank you.