The question is attached above. Please send step by step complete solution. I also request you please do not send any web link to this question because I am unable to  open the link every time  .

Asked by sudhanshubhushanroy | 14th Dec, 2017, 06:54: AM

Expert Answer:

begin mathsize 16px style straight C subscript 0 minus straight C subscript 2 plus straight C subscript 4 minus straight C subscript 6 plus..... equals 2 to the power of straight n over 2 end exponent cos open parentheses nπ over 4 close parentheses.......... left parenthesis straight i right parenthesis
straight C subscript 0 plus straight C subscript 2 plus straight C subscript 4 plus straight C subscript 6 plus..... equals 2 to the power of straight n minus 1 end exponent.............. left parenthesis ii right parenthesis
Add space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis
we space get
straight C subscript 0 plus straight C subscript 4 plus straight C subscript 8 plus.... equals 1 half open parentheses 2 to the power of straight n minus 1 end exponent plus 2 to the power of straight n over 2 end exponent cos open parentheses nπ over 4 close parentheses close parentheses
straight C subscript 0 plus straight C subscript 4 plus straight C subscript 8 plus...... equals fraction numerator 2 to the power of straight n minus 1 end exponent plus 2 to the power of straight n over 2 end exponent cos open parentheses nπ over 4 close parentheses over denominator 2 end fraction

straight C subscript 0 plus straight C subscript 4 plus straight C subscript 8 plus...... equals 2 to the power of straight n minus 1 end exponent over 2 plus fraction numerator 2 to the power of straight n over 2 end exponent cos open parentheses nπ over 4 close parentheses over denominator 2 end fraction
straight C subscript 0 plus straight C subscript 4 plus straight C subscript 8 plus...... equals 2 to the power of straight n minus 2 end exponent plus 2 to the power of straight n over 2 minus 1 end exponent cos open parentheses nπ over 2 close parentheses end style

Answered by Sneha shidid | 19th Dec, 2017, 10:25: AM