Question

Hello,Can you please help me with question# 11 ? it is express each sum using summation notation. Use 'i' as the index of th sum

Answer 1

Given:

The sum of terms

`4^3+5^3+6^3..........+13^3`

Required:

Find sum.

Step-by-step explanation:

We know sum of cube of first n terms of natural numbers

`\sum_{n\mathop{=}1}^(\infty)n^3=[(n(n+1))/(2)]^2`

Now,

`\begin{gathered} =(1^3+2^3+....+13^3)-(1^3+2^3+3^3) \\ =[(13(13+1))/(2)]^2-36 \\ =8281-36 \\ =8245 \end{gathered}`

Answer:

The sum of terms is 8245.