Given:
The equation is:
[tex]2\sum_{n=3}^7n^2=\sum_{n=3}^72n^2[/tex]
To find:
Whether the equation is true or not.
Solution:
We have,
[tex]2\sum_{n=3}^7n^2=\sum_{n=3}^72n^2[/tex]
Taking LHS, we get
[tex]LHS=2\sum_{n=3}^7n^2[/tex]
[tex]LHS=2[(3)^2+(4)^2+(5)^2+(6)^2+(7)^2][/tex]
[tex]LHS=2[9+16+25+36+49][/tex]
[tex]LHS=2[135][/tex]
[tex]LHS=270[/tex]
Taking RHS, we get
[tex]RHS=\sum_{n=3}^72n^2[/tex]
[tex]RHS=2(3)^2+2(4)^2+2(5)^2+2(6)^2+2(7)^2[/tex]
[tex]RHS=2(9)+2(16)+2(25)+2(36)+2(49)[/tex]
[tex]RHS=18+32+50+72+98[/tex]
[tex]RHS=270[/tex]
Here, [tex]LHS=RHS[/tex].
Therefore, the given equation is true.
