`1/10 + 1/40 + 1/88 + 1/154 + 1/238 + … + 1/754+1/928` Mong các bạn giúp 28/08/2021 Bởi Piper `1/10 + 1/40 + 1/88 + 1/154 + 1/238 + … + 1/754+1/928` Mong các bạn giúp
`1/10+1/40+1/88+1/154+1/238+…+1/754+1/928``=1/2.5+1/5.8+1/8.11+1/11.14+1/14.17+…+1/26.29+1/29.32``=1/3(3/2.5+3/5.8+3/8.11+3/11.14+3/14.17+…+3/26.29+3/29.32)``=1/3(1/2-1/5+1/5-1/8+1/8-1/11+1/11-1/14+1/14-1/17+…+1/26-1/29+1/29-1/32)``=1/3(1/2-1/32)``=1/3(16/32-1/32)``=1/3. 15/32``=5/32` Bình luận
Đáp án: `5/32` Giải thích các bước giải: Đặt biểu thức trên là `A` Ta có: `A × 3 = 3 × (1/10 + 1/40 + 1/88 + 1/154 + 1/238 + … + 1/754 + 1/928)` `A × 3 = 3/10 + 3/40 + 3/88 + 3/154 + 3/238 + … + 3/754 + 3/928` `A × 3` `=` $\dfrac{3}{2 × 5} + \dfrac{3}{5 × 8} + \dfrac{3}{8 × 11} + \dfrac{3}{11 × 14} + \dfrac{3}{14 × 17} + …+ \dfrac{3}{26 × 29} + \dfrac{3}{29 × 32}$ `A × 3 = 1/2 – 1/5 + 1/5 – 1/8 + 1/8 – 1/11 + … + 1/26 – 1/29 + 1/29 – 1/32` `A × 3 = 1/2 – 1/32 = 15/32` Vậy `A = 15/32 : 3 = 5/32` Bình luận
`1/10+1/40+1/88+1/154+1/238+…+1/754+1/928`
`=1/2.5+1/5.8+1/8.11+1/11.14+1/14.17+…+1/26.29+1/29.32`
`=1/3(3/2.5+3/5.8+3/8.11+3/11.14+3/14.17+…+3/26.29+3/29.32)`
`=1/3(1/2-1/5+1/5-1/8+1/8-1/11+1/11-1/14+1/14-1/17+…+1/26-1/29+1/29-1/32)`
`=1/3(1/2-1/32)`
`=1/3(16/32-1/32)`
`=1/3. 15/32`
`=5/32`
Đáp án:
`5/32`
Giải thích các bước giải:
Đặt biểu thức trên là `A`
Ta có:
`A × 3 = 3 × (1/10 + 1/40 + 1/88 + 1/154 + 1/238 + … + 1/754 + 1/928)`
`A × 3 = 3/10 + 3/40 + 3/88 + 3/154 + 3/238 + … + 3/754 + 3/928`
`A × 3` `=` $\dfrac{3}{2 × 5} + \dfrac{3}{5 × 8} + \dfrac{3}{8 × 11} + \dfrac{3}{11 × 14} + \dfrac{3}{14 × 17} + …+ \dfrac{3}{26 × 29} + \dfrac{3}{29 × 32}$
`A × 3 = 1/2 – 1/5 + 1/5 – 1/8 + 1/8 – 1/11 + … + 1/26 – 1/29 + 1/29 – 1/32`
`A × 3 = 1/2 – 1/32 = 15/32`
Vậy `A = 15/32 : 3 = 5/32`