2 years ago

Find the sum of (1-1/n) + (1-2/n) + (1 - 3/n)....upto n terms

Mathematics

1 answer:

bija089 [108]2 years ago

4 0

Answer:

Step-by-step explanation:

F = (1 - 1/n) + (1 - 2/n) + (1 - 3/n) + ...(1 - n/n)

= (1 + 1 ... + 1) - (1/n + 2/n + 3/n + ...n/n)

(there are n terms of 1)

= n - (1 + 2 + 3 + ... + n)/n

= n - [n x (n + 1)/2]/n

= n - [n x (n + 1)]/[2 x n]

= n - (n+1)/2

= (2n - n - 1)/2

= (n - 1)/2

Hope this helps!

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