1, 4, 9, 16, 25, 36, 49. The nth number is expressed as?

1, 4, 9, 16, 25, 36, 49. The nth number is expressed as?

Square of n

Calculate 1 △ (9-4) + 1 ± (16-4) + 1 ± (25-4) + 1 ^ (36-4) + 1 ^ (49-4) +. + 1 ^ (10000-4)

1/(k^2-4)=1/(k^2-2^2)=1/[(k-2)(k+2)]=[1/(k-2)-1/(k+2)]/4
So 1 △ 9-4 + 1 △ 16-4 + 1 △ 25-4 + 1 △ 36-4 + 1 △ 49-4 + 1 △ 10000-4
=(1/1-1/5)/4+(1/2-1/6)/4+(1/3-1/7)/4+(1/4-1/8)/4+(1/5-1/9)/4+(1/6-1/10)/4+…… +(1/93-1/97)/4+(1/94-1/98)/4+(1/95-1/99)/4+(1/96-1/100)/4+(1/97-1/101)/4+(1/98-1/102)/4
=[(1/1-1/5+1/3-1/7+1/5-1/9+…… +1/93-1/97+1/95-1/99+1/97-1/101)+(1/2-1/6+1/4-1/8+1/6-1/10+…… +1/94-1/98+1/96-1/100+1/98-1/102)]/4
=[(1/1+1/3-1/99-1/101)+(1/2+1/4-1/100-1/102)]/4
=(1/1+1/2+1/3+1/4-1/99-1/100-1/101-1/102)/4
In the back is pure calculation, if you just take a few decimal places, you'd better press the calculator
Approximately equal to 0.5109

Given x = 22 / 75, y = 25 / 44, find (x + y) - (X-Y)

（x+y）-（x-y） =[（x+y)+(x-y)][（x+y)-(x-y)]=(2x)(2y)=4xy=4×22/75×25/44=2/3