Sunday

March 29, 2015

March 29, 2015

Posted by **Aliyah** on Tuesday, August 23, 2011 at 1:06am.

: E (3r-5)= 3n^2-7n /2

r=1

- math -
**Reiny**, Tuesday, August 23, 2011 at 8:14amis that ∑(3r-5) as r goes from 1 to n ??

I will asssume it is

then ∑(3r-5) = (3n^2 - 7n)/2

Step 1 : test for n=1

LS = 3(1) - 5 = -2

RS = (3(1) - 7)/2 = -2

Step 2 : assume it true for n = k, that is ..

-2 + 1 + 4 + ... + (3k-5) = (3k^2 - 7k)/2

Step 3: prove it to be true for n = k+1

that is, prove

-2 + 1 + 4 + ... + (3k-5) + (3(k+1)-5) = (3(k+1)^2 - 7(k+1))/2

LS = (3k^2 - 7k)/2 + 3(k+1) - 5

= (3k^2 - 7k)/2 + 3k + 3 - 5

= (3k^2 - 7k + 6k - 4)/2

= (3k^2 - k - 2)/2

RS = (3(k+1)^2 - 7(k+1))/2

= (3k^2 + 6k + 3 - 7k - 7)/2

= (3k^2 - k -4)/2

Yeahhh!

- math -
**Aliyah**, Tuesday, August 23, 2011 at 5:30pmThank you so much!!!

**Answer this Question**

**Related Questions**

Math - Mathematical Induction - 3. Prove by induction that∑_(r=1)^n▒...

Calculus - Use mathematical induction to prove that the statement holds for all ...

AP Calc - Use mathematical induction to prove that the statement holds for all ...

math - use mathematical induction to prove -1/2^n = 1/2^n - 1

math - how do you prove that (a-1) divides ((a^n)-1) evenly using mathematical ...

Mathematical induction. I'm stuck. So far I have.. - For all integers n ≥ ...

Math - Use mathematical induction to prove that 2^(3n) - 3^n is divisible by 5 ...

math - Can anyone please help me with the following question: Prove by ...

Math - Observe that : 1/1*3= 1/3 1/1*3+ 1/3*5= 2/5 1/1*3+ 1/3*5+ 1/5*7= 3/7 1/1*...

Algebra - Prove by mathematical induction that 3^(3n+1) + 2^(n+1) is divisible ...