Đáp án:
Dãy số có $(52-2):2+1=26$ số hạng.
`(y+2)+(y+4)+(y+6)+...+(y+52)=780`
`=>26y+(2+4+6+...+52)=780`
`=>26y+((52+2)xx26)/2=780`
`=>26y+(52+2)xx13=780`
`=>26y+54xx13=780`
`=>26y+27xx26=780`
`=>26xx(y+27)=780`
`=>y+27=30`
`=>y=3`
Vậy `y=3`.
`b)``(1/2+1/4+1/8+1/16):y=1/(1xx2)+1/(2xx3)+...+1/(11xx12)`
`=>(1/2+1/4+1/8+1/16):y=1-1/2+1/2-1/3+...+1/11-1/12`
`=>(1/2+1/4+1/8+1/16):y=1-1/12`
`=>(1/2+1/4+1/8+1/16):y=11/12`
`=>A:y=11/12`
`=>A=1/2+1/4+1/8+1/16`
`=>2A=2xx(1/2+1/4+1/8+1/16)`
`=>2A=1+1/2+1/4+1/8`
`=>2A-A=(1+1/2+1/4+1/8)-(1/2+1/4+1/8+1/16)`
`=>A=1-1/16`
`=>A=15/16`
`=>15/16:y=11/12`
`=>y=45/44`
Vậy `y=45/44`.
`c)` Dãy số có $(26-4):2+1=12$ số hạng.
`=>(y+4)+(y+6)+(y+8)+...+(y+26)=210`
`=>12y+(4+6+8+...+26)=210`
`=>12y+((26+4)xx12)/2=210`
`=>12y+30xx6=210`
`=>12y+15xx12=210`
`=>12xx(y+15)=210`
`=>y+15=17,5`
`=>y=5/2`
Vậy `y=5/2`.
`d)``(1/2+x)+(1/4+x)+(1/8+x)+(1/16+x)=1`
`=>4x+(1/2+1/4+1/8+1/16)=1`
`=>4x+A=1`
`=>A=1/2+1/4+1/8+1/16`
`=>2A=2xx(1/2+1/4+1/8+1/16)`
`=>2A=1+1/2+1/4+1/8`
`=>2A-A=(1+1/2+1/4+1/8)-(1/2+1/4+1/8+1/16)`
`=>A=1-1/16`
`=>A=15/16`
`=>4x+15/16=1`
`=>4x=1/16`
`=>x=1/64`
Vậy `x=1/64`.