nC1 -nC3 +nC5- so on
i know, iota will be involved in here, but im confused as i think it depends whether n is odd or even, it turns out to be different in each case. Any hint will be appreciated. Thanks.
2026-02-23 12:05:31.1771848331
find the sum of the given series.
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its binomial expansion for the real values of $$(1+i)^n=(^n_0)i^0+(^n_1)i^1+(^n_2)i^2+(^n_3)i^3+(^n_4)i^4+(^n_5)i^5+....$$ $$=(^n_0) +(^n_1)i^1-(^n_2)-(^n_3)i+(^n_4) +(^n_5)i +....$$
if we take the imaginary term from the series then it will become $$= (^n_1) -(^n_3) +(^n_5)+....$$