Question

Can you please convert the following series into summation notation?

Write each series in summation notation beginning with k = 1.


1.
`image`


3.
`9-16+25-36+49-64`


4.
`3+(3)/(2) +1+(3)/(4)+(3)/(5)`

Answer 1

`\displaystyle\\1)\\\\(1)/(2)+(2)/(3)+(3)/(4)+(4)/(5)+(5)/(6)=\boxed{\sum _(k=1)^(5){(k)/(k+1)}}\\\\\\2)\\\\ -11+12-13+14-15+16=\boxed{\sum _(k=1)^(6){(-1)^k\cdot(10+k)} }`

`\displaystyle\\3)\\9-16+25-36+49-64=\boxed{\sum_(k=1)^(6){(-1)^(k+1)\cdot(k+2)^2}}\\\\\\4)\\\\3+(3)/(2)+1+(3)/(4)+(3)/(5)=(3)/(1)+(3)/(2)+(3)/(3)+(3)/(4)+(3)/(5)=\boxed{\sum_(k=1)^(5){(3)/(k)}}`