1 4 2 4 3 4 n 4 formula
Asked by admin @ in Math viewed by 436 People
Find the sum of 4-1/n, 4-2/n, 4-3/n up to the nth term
Answered by admin @
Hello users .....
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
we have to find:-
the sum of 4-1/n, 4-2/n, 4-3/n = ?
solution:-
we know that :
1 + 2 +3 + 4 +5 +6 + ...........+ n = n(n +1) / 2
and
1 + 1+ 1 + 1 + 1 + .............+ n = n
Here,
sum of 4-1/n, 4-2/n, 4-3/n up to the nth term
= (4 + 4 + 4 + 4 + 4 + ......... upto n terms) + (-1/n - 2/n - 3/n - ..........upto n terms)
= 4 ( 1+1+1+1.......... upto n terms) - 1/n (1 + 2 + 3 +4 .........upto n terms)
= 4 n - 1/n × n(n +1)/2
= 4n - (n+1)/2
= [ 8n - (n+1) ] / 2 .......taking L.C.M
=( 7n - 1) / 2 Answer
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
@@ hope it helps @@
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