Q. 13

Prove that (1 + i2 + i4 + i6 + i8 + …. + i20) = 1.

L.H.S = (1 + i2 + i4 + i6 + i8 + …. + i20)

=

= 1 + -1 +1 + -1 + ……….. + 1

As there are 11 times 1 and 6 times it is with positive sign as =1 as this is the extra term and there are 5 times 1 with negative sign

So, these 5 cancel out the positive one leaving one positive value i.e. 1

=

L.H.S = R.H.S

Hence proved.

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