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(61)/(n=1)i^(n)...

(61)/(n=1)i^(n)

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If I_(n)=int_(0)^((pi)/(4))tan^(n)xdx,(n>1 and is an integer),then I_(n)+I_(n-2)=(1)/(n+1)I_(n)+I_(n-2)=(1)/(n-1)I_(2)+I_(4),I_(4)+I_(6),..., are in H.P.(1)/(2(n+1))

Q.sum_(n=1)^(13)(i^(n)+i^(n+1))=(-1+i),n in N

Show that (1-i)^(n)(1-(1)/(i))^(n)=2^(n) for all n in N

Find the integral values of n for the equations : (a) (1+i)^(n)=(1-i)^(n) (b) (1-i)^(n)=2^(n)

Evaluate sum_(n=1)^(13)(i^(n)+i^(n+1)), where n in N

If n in Z , then (2^(n))/(1+i)^(2n)+(1+i)^(2n)/(2^(n)) is equal to

If I_(n)=int cos^(n)x dx . Prove that I_(n)=(1)/(n)(cos^(n-1)x sinx)+((n-1)/(n))I_(n-2) .

If I_(n)=int cos^(n)x dx . Prove that I_(n)=(1)/(n)(cos^(n-1)x sinx)+((n-1)/(n))I_(n-2) .

If I_(n)=int cos^(n)x dx . Prove that I_(n)=(1)/(n)(cos^(n-1)x sinx)+((n-1)/(n))I_(n-2) .

If ((1+i)/(1-i))^(n) = -1, n in N , then least value of n is