上 prove that 1 2 3 ... n=n(n 1)/2 283037-12.prove that ((2)^(n)+(2)^(n-1))/(2n+1)-2^(n))=(3)/(2)

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12.prove that ((2)^(n)+(2)^(n-1))/(2n+1)-2^(n))=(3)/(2)

12.prove that ((2)^(n)+(2)^(n-1))/(2n+1)-2^(n))=(3)/(2)-

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Incoming Term: prove that 1+2+3+...+n=n(n+1)/2, prove for each natural number n≥1n≥1 that 1+2+3+⋯+n=n(n+1)2, prove that 1^3+2^3+3^3+...+n^3=n^2(n+1)^2/4, prove by exhaustion that 1+2+3+...+n=n(n+1)/2 for positive integers from 1 to 6 inclusive, prove that 1^2+2^2+3^2+⋯+n^2=(n(n+1)(2n+1))/6, prove that 1.2+2.3+⋯..+n(n+1)=(n(n+1)(n+2))/3, prove that 2^n+2^n-1/2n+1-2^n=3/2, use induction to prove that 1^3+2^3+3^3+...+n^3= ((n(n-1)/2)^2, 12.prove that ((2)^(n)+(2)^(n-1))/(2n+1)-2^(n))=(3)/(2), how to prove n(n+1)/2,