find the value of :1+ i2+i4+ i6+i8 ...+i20.

  • 3
consider it as an AP excluding 1
as we know that i = _/1 = root 1 = 1
then...
AP = 2 + 4 + 6 + 8 + ... + 20
here:
a=2 , d= A2 - A1 = 4 - 2 = 2
using formulae
An = a+(n-1)d
20 = 2 + (n-1)2
20 - 2 = (n-1)2
18 = (n-1)2
18 ÷ 2 = n-1
9 = n-1
9+1 = n
10 = n

now using formula..
Sn = n÷2 [2a + (n-1)d ]
S10 = 10÷2 [ 2×2+(10-1)2]
= 5 [4 + 9×2]
= 5 [ 4 + 18]
= 5 [22]
= 5×22
=110
now add 1 that we have excluded at begining....
110+1 = 111
Therefore answer is 111
  • -5
thanks☺
  • -5
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