Đáp án:
`a,A=1023/1024`
`b,B=7/8`
Giải thích các bước giải:
`a,A= 1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512+1/1024`
`⇒A= 1/2+1/2^2+1/2^3+1/2^4+1/2^5+1/2^6+1/2^7+1/2^8+1/2^9+1/2^10`
`⇒2A=1+1/2+1/2^2+1/2^3+1/2^4+1/2^5+1/2^6+1/2^7+1/2^8+1/2^9`
`⇒2A-A=(1+1/2+1/2^2+1/2^3+1/2^4+1/2^5+1/2^6+1/2^7+1/2^8+1/2^9)-(1/2+1/2^2+1/2^3+1/2^4+1/2^5+1/2^6+1/2^7+1/2^8+1/2^9+1/2^10)`
`⇒A=1-1/2^10`
`⇒A=1-1/1024=1023/1024`
`b, B=1/2+1/6 + 1/12+ 1/20+ 1/30+ 1/42+ 1/56 `
`⇒B=1/1.2+1/2.3 + 1/3.4+ 1/4.5+ 1/5.6+ 1/6.7+ 1/7.8 `
`⇒B=1-1/2+1/2-1/3 + 1/3-1/4+ 1/4-1/5+ 1/5-1/6+ 1/6-1/7+ 1/7-1/8 `
`⇒B=1+(-1/2+1/2)+(-1/3 + 1/3)+(-1/4+ 1/4)+(-1/5+ 1/5)+(-1/6+ 1/6)+(-1/7+ 1/7)-1/8 `
`⇒B=1+0+0+0+0+0+0-1/8 `
`⇒B=1-1/8=7/8`
