2^2/(2^2-1) ,4^2/(4^2-1) ,6^2/(6^2-1) ,8^2/(8^2-1)…… How to sum this sequence?

2^2/(2^2-1) ,4^2/(4^2-1) ,6^2/(6^2-1) ,8^2/(8^2-1)…… How to sum this sequence?

Sn=2^2/(2^2-1)+4^2/(4^2-1)+6^2/(6^2-1)+…… +n^2/((2n)^2-1)
=[1+1/(2^2-1)]+[1+1/(4^2-1)]+[1+1/(6^2-1)]+…… +[1+1/((2n)^2-1)]
=n+0.5×[2/(2-1)×(2+1)+2/(4-1)×(4+1)+2/(6-1)×(6+1)+…… +2/(2n-1)×(2n+1)]
=n+0.5×[(3-1)/1×3+(5-3)/3×5+(7-5)/5×7+…… +((2n+1)-(2n-1))/(2n-1)×(2n+1)]
=n+0.5×[(1/1-1/3)+(1/3-1/5)+(1/5-1/7)+…… +(1/(2n-1)-1/(2n+1)]
=n+0.5×[1-1/(2n+1)]
=n+n/(2n+1)

Linear algebra problem: what happens when a row matrix is multiplied by a column matrix or when a column matrix is multiplied by a row matrix
What happens when a row matrix is multiplied by a column matrix or when a column matrix is multiplied by a row matrix
What's the difference

Matrix multiplication is based on multiplication rules
Rule: for a matrix with M rows and N columns, a = (a)_ {ij}), matrix B = (b) of N rows and s columns_ In terms of {JK},
AB=C=(c_ {IK}) is a matrix with M rows and s columns, and the element C in the position of I row and K column_ {IK} is the i-th line element a of matrix A_ {i1},...,a_ {in} and the nth column element a of B_ {1n},...,a_ {ns} corresponds to the sum of products

A total of 47 people in the class went out to travel, and a total of 8 boats were rented. Each boat was full of people. The big boat could take 7 people, and the small boat could take 4 people. How many boats did the big boat and the small boat rent?
Please give the formula instead of solving the equation
Don't solve the equation

Suppose it's all big boats;: 7x8 = 56 people more than the actual: 56-47 = 9 people transfer to small boats: 9 / (7-4) = 3 big boats: 8-3 = 5

LIM (sin2x / x) (x tends to 0), LIM (arctan2x / x) (x tends to ∞)

LIM (sin2x / x) (x tends to 0)
=Lim2 (sin2x / 2x) (2x tends to 0)
=2
LIM (arctan2x / x) (x tends to ∞)
=0
(because arctan2x tends to π / 2 and the denominator is infinite, the ratio is 0)

What is the square of 6 plus the square of 7?

Square of 6 plus square of 7
=36+49
=85

How many classes does he have every day?

How many periods does he get each day?
How many lessons does he have every day?

How many kilometers is a kilometer? How many meters is a mile? How many miles is a kilometer?

One kilometer is one kilometer, one mile is 500 meters, one kilometer equals two miles

Design a calculation 1 + 3 + 5 + 7 + The algorithm of 99?

1+3+5+7+… 99 = (1 + 99) × 50 / 2 = 2500
1+3+5+7+… 99=（1+99)+（3+97)+（5+95)+… （49+51)=100×25=2500

Please tell me the meaning of some English words!
What do you mean by wheel, chain, tire, bell and seat,

Wheel: Wheel: Chain: Tire: Bell: ring seat: seat

The sum of the first n terms of the arithmetic sequence {an} is Sn, S4 = - 62, S6 = - 75. Let BN = | an}, find the sum of the first n terms of the sequence {BN} and TN

This is where we get d = 3, A1 = -20, an = 3, A1 = -20, an = 3n-23, where the starting point of N + 1 is greater than zero, then an = -20 + 3 (n-1) ≤ 0An + 3 (n-1) (n-1) ≤ 0 (n-1) (n-1) ≤ 0An + 1 (n-1) ≤ 0An + 1 (n-1) (n-1) ≤ 0An (n-1) (n-1) ≤ n (n-1) ≤ n-233, n = 7, that is, a 7 & lt; 0, a 8 & gt; 0; 0; when 1 ≤ n ≤ 7, when 1 ≤ n ≤ 7 ≤ n ≤ 7, TN = - Sn = 43n-3n-3n = 43n-3nn22, when n ≥ 8, and when n ≥ 8, TN = 32n2-43n2-432n-432n-432n-432n-432n-432n-432n + 154.2n + 154. (n ≥ 8)