`3/2 + 3/4 + 3/8 + 3/16 + 3/32 + 3/64`
`= (3 xx 32)/64 + (3xx 16)/64 + (3 xx 8)/64 + (3xx 4)/64+ (3xx2)/64 + 3/64`
`= (3 xx 32 + 3 xx 16 + 3 xx 8 + 3 xx 4 + 3 xx 2 + 3)/64`
`= (3 xx (32 + 16 + 8 + 4 + 2 + 1))/64`
`= (3 xx 63)/64`
`= 189/64`
`3/2 + 3/4 + 3/8 + 3/16 + 3/32 + 3/64`
`= 3 * (1/2+1/4+1/8+1/16+1/32+1/64)`
`= 3*(32/64+16/64+8/64+4/64+2/64+1/64)`
`= 3*63/64`
`= 189/64`
`5/2+5/6+5/12+5/20+5/30+5/42`
`= 5 * (1/2+1/6+1/12+1/20+1/30+1/42)`
`= 5*(1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7))`
`= 5*(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7)`
`= 5*(1-1/7)`
`= 5*6/7`
`= 30/7`
`5/2 + 5/6 + 5/12 + ... + 5/42`
`= 5 xx (1/2 + 1/6 +1/12 + ... + 1/42)`
`= 5 xx (1/(1xx2) + 1/(2xx3) +1/(3xx4) + ... + 1/(6xx7))`
`= 5 xx (1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/6 - 1/7) `
`= 5 xx (1 - 1/7) `
`= 5 xx 6/7`
`= 30/7`
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