# calculus

write the sigma notation.

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

You could use capatil E as a sigma.

Please help!!

1. 👍
2. 👎
3. 👁
1. 5 = 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

1. 👍
2. 👎

## Similar Questions

1. ### Math

How do I use the sigma notation to express the series : 1+5+25+125+625+3125?

2. ### math

rewrite the series in sigma notation 4+16+64+...+256+1024

3. ### Calculus

Express the following in Sigma notation 2+8+18+32+50+72

4. ### algebra

rewrite each series using sigma notation 9) 1+4+9+16+25+36 and 10) 4+8+12+16+20

1. ### Calculus

Express the sum using sigma notation 1+ 5/6+ 6/8+ 7/10 + 8/12

2. ### math

Write the series as a summation in sigma notation 6 + 12 + 24 + 48

3. ### Math

Write 10+6+2+(-2)+(-6)+(-10)+(-14) in sigma notation.

4. ### Calculus

Express the following in Sigma notation 2+8+18+32+50+72

1. ### Calculus - Alternating Series Test

Determine whether the infinite series, sigma(((-1)^(n+1))/n)^2 converges or diverges. My professor gave these in a problem set after he taught the alternating series test. Simplying the series we get, sigma(((-1)^(n+1))/n)^2

2. ### math

use sigma notation to write the maclaurin series for the function ln(1+x)

3. ### Calculus

Express the um using sigma notation: 1 +3/4 +5/9+ 7/16+ 9/25

4. ### Math

Write 5+7+9+11+13+15+17 in sigma notation.