Hello,
We suppose the property true for n:
1²+2²+...+n²=n(n+1)(2n+1) / 6
and we are going to demonstrate that the property is true for n+1:
1²+2²+..+(n+1)²=(n+1)*(n+2)*(2n+3)/6
![1^2+2^2+...+n^2+(n+1)^2\\\\=n*(n+1)*(2n+1)/6+(n+1)^2\\\\=(n+1)/6*[n(2n+1)+6n+6]\\\\=(n+1)/6*(2n^2+7n+6)\\\\=(n+1)(n+2)(2n+3)/6\\](https://tex.z-dn.net/?f=1%5E2%2B2%5E2%2B...%2Bn%5E2%2B%28n%2B1%29%5E2%5C%5C%5C%5C%3Dn%2A%28n%2B1%29%2A%282n%2B1%29%2F6%2B%28n%2B1%29%5E2%5C%5C%5C%5C%3D%28n%2B1%29%2F6%2A%5Bn%282n%2B1%29%2B6n%2B6%5D%5C%5C%5C%5C%3D%28n%2B1%29%2F6%2A%282n%5E2%2B7n%2B6%29%5C%5C%5C%5C%3D%28n%2B1%29%28n%2B2%29%282n%2B3%29%2F6%5C%5C)
Answer:
The 9th term is 17179869184
Step-by-step explanation:
Here we have that;
The divisors of 1 = 1 which is 1 less than 1*2
The sum of the divisors of 2 = 1 + 2 = 3 which is 1 less than 2*2
The sum of the divisors of 4 = 1 + 2 + 4 which is 1 less than 4*2
The sum of the divisors of 8 = 1 + 2 + 4 + 8 which is 1 less than 8*2
The sum of the divisors of 32 = 1 + 2 + 4 + 8 + 16 + 32 which is 1 less than 32*2
The sum of the divisors of 256 = 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 which is 1 less than
The next numbers are therefore,
32 × 256 = 8192
256 × 8192 = 2097152 and the 9th term is therefore;
8192 × 2097152 = 17179869184.
<span><span>Solve the system for x and y.</span><span>2y = x + 8</span><span>2y − 10 = 2x</span> <span>A) x = </span>−<span>3, y = 2</span> <span>B) x = </span>−<span>2, y = 3</span> <span>C) x = </span>−<span>5, y = 2</span> <span>D) x = 0, y = -5</span></span>
Answer:
500 pages
Step-by-step explanation:
310 ÷ 62 to find 1% which equals 5. Then multiply 5 by 100 to get 500
Answer:
3,006.0578 is your answer.
Step-by-step explanation:
3 × 1000 + 6 × 100 + 3 × 10 + 7 × 0.1 + 2 × 100 + 8 × 0.0001 = 3,006.0578
