Question

1/2*1+1/2*3+...+1/24*25=

Answer 1

Răspuns:

Explicație pas cu pas:

1/1*2 = 1/1 - 1/2

1/2*3 = 1/2 - 1/3

......

1/24*25 = 1/24 - 1/25

_______________

1/1*2 + 1/2*3 + ...+ 1/24*25 = 1/1 - 1/2 + 1/2 - 1/3 + ...+ 1/24 - 1/25

= 1/1 - 1/25 = 25/25 - 1/25 = 24/25

Answer 2

Răspuns:

24/25

Explicație pas cu pas:

k=24

∑1 / k(k+1) =

k=1

∑(1/k - 1/ k+1) =

1 - 1/2 +

1/2 - 1/3 +

1/3 - 1/4 +

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1/24 - 1/25 = (se reduc toti termenii cu cifre ingrosate)

1 - 1/25 =

24/25.