Ai giỏi toán học thì làm bài này giúp mình ạ:
Chứng minh rằng: $\frac{1}{26}$ + $\frac{1}{27}$ + $\frac{1}{28}$ +…+ $\frac{1}{50}$ = 1 – $\frac{1}{2}$ + $\frac{1}{3}$ – $\frac{1}{4}$ +…+ $\frac{1}{49}$ – $\frac{1}{50}$ 1
Ai giỏi toán học thì làm bài này giúp mình ạ:
Chứng minh rằng: $\frac{1}{26}$ + $\frac{1}{27}$ + $\frac{1}{28}$ +…+ $\frac{1}{50}$ = 1 – $\frac{1}{2}$ + $\frac{1}{3}$ – $\frac{1}{4}$ +…+ $\frac{1}{49}$ – $\frac{1}{50}$ 1
Ta có :1/26 + 1/27 + … + 1/50 – (1-1/2+1/3-1/4+…+1/49-1/50)
=1/26+1/27+…+1/50 + (1/26-1/27+….-1/49+1/50) + (-1/13+1/14-….+1/24-1/25)+(-1/7+1/8-….. + 1/12) + (1/6-1/5+1/4)+(1/2-1)
=1/13+1/14+…+1/25+ (-1/13+1/14-….+1/24-1/25)+(-1/7+1/8-….. + 1/12) + (1/6-1/5+1/4)+(1/2-1)
=1/7+1/8+…+1/12 + (-1/7+1/8-…-1/11 + 1/12) + (1/6-1/5+1/4)+(1/2-1)
=1/4+1/5+1/6 +(1/6-1/5+1/4)+(1/2-1)
=1/2+1/2-1
=0
Vậy 1/26 + 1/27 + 1/28 +…..+ 1/49 +1/50 = 1- 1/2 +1/3 – 1/4 +….+ 1/49 – 1/50
`1- 1/2+ 1/3 – 1/4 +….+1/49 -1/50`
`= (1+ 1/3 +…+1/49) – (1/2 + 1/4 + 1/6….+1/50)`
`= (1+1/2 +1/3 + …+1/48+1/49 + 1/50) – 2(1/2 + 1/4 +1/6…+1/50)`
`= 1 + 1/2 + 1/3 +…+1/48 + 1/49 + 1/50 – 1 – 1/2 -1/3 -…-1/25`
`= 1/26 + 1/27 +…+1/50`