In a formula, if the ratio of two ratios is equal to 4 and the external terms of the ratio are 8 and 6, write the formula. If the internal terms are 8 and 6, write the formula

In a formula, if the ratio of two ratios is equal to 4 and the external terms of the ratio are 8 and 6, write the formula. If the internal terms are 8 and 6, write the formula

8:2=24:6
32:8=6:1.5

What is 1 times 2 + 2 times 3 + 3 times 4 + 4 times 5 +. + 100 times 101

General items:
ak=k(k+1)=k^2+k
1×2+2×3+...+100×101
=(1^2+2^2+...+100^2)+(1+2+...+100)
=100×101×201/6+100×101/2
=343400
Two formulas are used here
1^2+2^2+...+n^2=n(n+1)(2n+1)/6
1+2+...+n=n(n+1)/2

Three and a half times 101 minus 0.35 equals

Formula = 3.5 * 101-0.35 = 353.5-0.35 = 353.15

How much is 1:2 by 1:3 by 1:4 by 1:5 by... By 1:100 by 1:101?

=3/2×4/3×5/4×…… ×102/101
Approximate points
=102/2
=51