Question

2^2+4^2+6^2+..+16^2+18^2

Answer 1

\(2^2+4^2+6^2++...+16^2+18^2\)
\(=2^2.\left(1+2^2+3^2+...+8^2+9^2\right)\)
\(=4\times\dfrac{9\times\left(9+1\right)\times\left(2\times9+1\right)}{6}\)
\(=4\times285\)
\(=1140\)

Answer 2

1140

Answer 3

\(2^2+4^2+6^2+...+16^2+18^2\)

\(=2^2.1+2^2.2^2.3^2+...+2^2.8^2+2^2.9^2\)

\(=2^2\left(1^2+2^2+3^2+...+8^2+9^2\right)\)

\(=4.285\)

\(=1140\)

Answer 4

\(=2^2.1+2^2.2^2.3^2+....+2^2.8^2+2^2.9^2\)

\(=2^2\left(1^2+2^2+3^2+...+8^2+9^2\right)\)

\(=4.285\)

\(\Rightarrow1140\)