Question

Help needed!! Mark as brainliest

Answer 1

Given:

The equation is:

$2\sum_{n=3}^7n^2=\sum_{n=3}^72n^2$

To find:

Whether the equation is true or not.

Solution:

We have,

$2\sum_{n=3}^7n^2=\sum_{n=3}^72n^2$

Taking LHS, we get

$LHS=2\sum_{n=3}^7n^2$

$LHS=2[(3)^2+(4)^2+(5)^2+(6)^2+(7)^2]$

$LHS=2[9+16+25+36+49]$

$LHS=2[135]$

$LHS=270$

Taking RHS, we get

$RHS=\sum_{n=3}^72n^2$

$RHS=2(3)^2+2(4)^2+2(5)^2+2(6)^2+2(7)^2$

$RHS=2(9)+2(16)+2(25)+2(36)+2(49)$

$RHS=18+32+50+72+98$

$RHS=270$

Here, $LHS=RHS$.

Therefore, the given equation is true.