Simplify the slope of AC
1 answer:
Answer:
Step-by-step explanation:
A is on the same point on the x-axis as B and the same point on the y-axis as D
- Therefore, the coordinate of A is (0,0)
C is on the same point on the x-axis as D and the same point on the y-axis as B.
- Therefore, the coordinate of C is (a,a)
We are to determine the slope of the line joining A to C.
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The sum of the first n odd numbers is n squared! So, the short answer is that the sum of the first 70 odd numbers is 70 squared, i.e. 4900.
Allow me to prove the result: odd numbers come in the form 2n-1, because 2n is always even, and the number immediately before an even number is always odd.
So, if we sum the first N odd numbers, we have
The first sum is the sum of all integers from 1 to N, which is N(N+1)/2. We want twice this sum, so we have
The second sum is simply the sum of N ones:
So, the final result is
which ends the proof.