Math, asked by ttt14, 1 year ago

find the sum of n terms of the series 4 minus 1 upon 1n + 4 minus 2 upon 10 + 4 minus 3 upon 10 + 4 minus 4 Upon A

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Answered by Mizhaan
10
this is the summation of 4-r/n from r = 1 to r=n.
as we can see 4 is being added n times
hence the sum will have a term of 4n.
now we'll take -1/n common from those terms which will leave us to the famous sum of natural numbers which is n(n+1)
hence our sum will be :
4n -1/n x n(n+1)
solve and get 3n-1

Mizhaan: apply summation
Mizhaan: summ(4-r/n) (r from 1 to n)
Mizhaan: = 4n -1/n*summ(r)
Mizhaan: summ(r) = n(n+1)/2
Mizhaan: substitute
Mizhaan: you get 4 - (n+1)/2
Mizhaan: simplify to get (7-n)/2
Mizhaan: oh my bad
Mizhaan: ill send a pic
Mizhaan: you get final answer as (7n -1)/2 ***
Answered by nsain25
19
hope this helps........
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