设f(n)=cosnπ/2,则f(25)+f(26)+f(27)+···+f(42)=
题目
设f(n)=cosnπ/2,则f(25)+f(26)+f(27)+···+f(42)=
答案
f(n) + f(n+1) + f(n+2)+f(n+3) = [f(n) + f(n+2)] + [f(n+1) + f(n+3)]= [cosnπ/2 + cos(n+2)π/2] + [cos(n+1)π/2 + cos(n+3)π/2] = cosnπ/2 + cos(nπ/2 + π) + cos(n+1)π/2 + cos[(n+1)π/2 + π] = cosn...
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