Question

plz answer the question



Evaluate:



(1³+2³+3³) to the power of -5/2​

Answer 1

Step-by-step explanation:

Lets start by taking a quick glance at the recurring pattern of 13+23+33+...n3 :

13=1=12

13+23=1+8=9=32

13+23+33=1+8+27=36=62

Do you see a pattern yet? The pattern is we are summing all of the values up to n and then squaring n.

Let’s see if we can prove it!

Assume: 13+23+...+n3=((n∗(n+1))/2)2

1=13=((1∗(2))/2)2=1 , therefore the base case holds.

13+23+...+n3+(n+1)3=((n∗(n+1))/2)2+(n+1)3

=((n∗(n+1))/2)2+(n3+3n2+3n+1)=1/4∗n4+3/2∗n3+13/4∗n2+3n+1 , which indeed equals ((n+1)∗(n+2)/2)2

Therefore, by the inductive hypothesis, 13+23+...n3=(n∗(n+1)/2)2

Answer 2

See the attachment

hope it helps you :-)