Sequence summation ∑ (2 / 7 ^ N-5 / 2 ^ n), (that is to sum 2 / N of 7 minus 5 / N of 2) ∑(2/7^n-5/2^n)=(2/7+2/7^1+2/7^3.+2/7^n)-(5/2+5/2^2+5/2^3+.5/2^n)= 1/3[1-(1/7)^n]-5[1-(1/2)^n]=1/3-5 What is the sum formula? What is the formula? Where do the 1 / 3 and 5 come from?

Sequence summation ∑ (2 / 7 ^ N-5 / 2 ^ n), (that is to sum 2 / N of 7 minus 5 / N of 2) ∑(2/7^n-5/2^n)=(2/7+2/7^1+2/7^3.+2/7^n)-(5/2+5/2^2+5/2^3+.5/2^n)= 1/3[1-(1/7)^n]-5[1-(1/2)^n]=1/3-5 What is the sum formula? What is the formula? Where do the 1 / 3 and 5 come from?

Equal ratio sequence
2 / 7 ^ n is an equal ratio sequence with a common ratio of 1 / 7
5 / 2 ^ n is an equal ratio sequence with a common ratio of 1 / 2
Summation formula of equal ratio sequence:
Sn=a1(1-q^n)/(1-q) =(a1-an×q)/(1-q) (q≠1)
(q is the common ratio, n is the number of terms)