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Question

Sum upto 100 term of the series i+2i2+3i3+ is

A
50(1i)
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B
25i
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C
25(1+i)
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D
100(1i)
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Solution

The correct option is A 50(1i)
S=i+2i2+3i3+ 100i100(1)
Si= i2+2i3++99i100+100i101(2)
Subtracting Equation (2) from equation (1), we get
S(1i)=i+i2+i3+ i100100i101
Sum of n terms of G.P Sn=a(1rn)1r
Here, a=i,r=i,n=100
S(1i)=i(1i100)1i100i100i
[i100=(i4)25=1]
Now, S(1i)=0100i
S=100(i1i)
S=100(i(1+i)2)
S=50(1i)

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