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.
We know that Bob and Caitlyn are playing a trading-card game. Between them, they have 81 cards. <span>Bob has 7 fewer cards than Caitlyn. Since Bob has 7 cards fewer them Caitlyn we have to divide by 2 and subtract 7.
81 / 2 = 40 [rounded]
40 - 7 = cards Bob has
= 33 cards bob has
</span>
Answer:
9y +9x - 10a-10c -10b = 105
Step-by-step explanation:
Given
a+b+c = -6 and x+y = 5
We have to find 9y +9x - 10a-10c -10b
Rearranging the terms
9x+9y-10a-10b-10c
Simplifying will give us:
= 9 (x+y) - 10(a+b+c)
Putting the values of x+y and a+b+c
= 9(5) -10(-6)
=45+60
=105
Therefore,
9y +9x - 10a-10c -10b = 105 ..
Part A:5=2x^2-x^2+13
5=x^2+13
0=x^2+13-5
0=x^2+8
Part B:5=2x^3-x^3+13
5=x^3+13
0=x^3+13-5
0=x^3+8
