Saturday

February 28, 2015

February 28, 2015

Posted by **Meme J** on Wednesday, September 5, 2012 at 12:39am.

5^2+6^2+7^2+...+14^2

You could use capatil E as a sigma.

Please help!!

- calculus -
**Bosnian**, Wednesday, September 5, 2012 at 1:48am5 = 1 + 4

6 = 2 + 4

7 = 3 + 4

...

14 = 10 + 4

5 ^ 2 + 6 ^ 2 + 7 ^ 2 + ... + 14 ^ 2 =

( 1 + 4 ) ^ 2 + ( 2 + 4 ) ^ 2 + ( 3 + 4 ) ^ 2 + ... + ( 10 + 4 )^ 2 =

E ( k + 4 ) ^ 2 from n = 1 to n = 10

________________________________________

( k + 4 ) ^ 2 = k ^ + 2 * k * 4 + 4 ^ 2 =

k ^ 2 + 8 k + 16

_______________________________________

E ( k + 4 ) ^ 2 from n = 1 to n = 10 =

E k ^ 2 from n = 1 to n = 10 + 8 * E k from n = 1 to n = 10 + E 16 from n = 1 to n = 10 =

E k ^ 2 from n = 1 to n = 10 + 8 * E k from n = 1 to n = 10 + 10 * 16 =

E k ^ 2 from n = 1 to n = 10 + 8 * E k from n = 1 to n = 10 + 160

________________________________________

E k ^ 2 from n = 1 to n = 10

= n * ( n + 1 ) * ( 2 n + 1 ) / 6 =

10 * ( 10 + 1 ) * ( 2 * 10 + 1 ) / 6 =

10 * 11 * 21 / 6 = 2310 / 6 = 385

_______________________________________

E k from n = 1 to n = 10

= n * ( n + 1 ) / 2 = 10 * 11 / 2 = 110 / 2 = 55

_______________________________________

E ( k + 4 ) ^ 2 from n = 1 to n = 10

= E k ^ 2 from n = 1 to n = 10 + 8 * E k from n = 1 to n = 10 + 160

= 385 + 8 * 55 + 160 = 385 + 440 + 160 = 985

**Answer this Question**

**Related Questions**

math - I just need help with this. Write the series in sigma notation. 1/4 + 1/2...

math - I just need help with this. Write the series in sigma notation. 1/4 + 1/2...

Pre-CalcPlease check - Please check: 1.Write in expanded form: this is a sigma ...

Algebra II - Please help-I need to write 4+6+8+10 in sigma notation would it be ...

further mathematics - The roots of the eqn, x^4 + px^3 + qx^2 + rx + s = 0 where...

Math - Write the sum (in sigma notation) 1 + 3/2 + 2 + 5/2 + 3 + 7/2 + 4 Sigma ...

Calculus - So this one is confusing me: limit of n as it approaches infinity of...

Maths - Express the sum using summation notation: 1 - 1/2 + 1/3 - 1/4 + 1/5...

Maths - Express the sum using summation notation: 1 - 1/2 + 1/3 - 1/4 + 1/5...

Maths - Express the sum using summation notation: 1 - 1/2 + 1/3 - 1/4 + 1/5...