1204 HWK MrG 2013.0403

#p843 #10) 1+5+5^2+5^3+...+5^(n-1)=(1/4)(5^n-1) f(n)=(1/4)*(5^n-1) show(f(1)) show(f(2)) 

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#10)prove: 1+5+5^2+5^3+...+5^(n-1)+5^n=(1/4)(5^(n+1)-1) #10)assume:1+5+5^2+5^3+...+5^(n-1) =(1/4)(5^n-1) #10)show: 5^n = (1/4)(5^(n+1)-1) - (1/4)(5^n-1) ((1/4)*(5^(n+1)-1) - (1/4)*(5^n-1)).simplify_rational() 

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#5)2+5+8+...+3n-1=(1/2)n(3n+1) f(n)=(1/2)*n*(3*n+1) show(f(1)) show(f(2)) 

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#5) show: 2+5+8+...+3n-1+3n+2 = (1/2)(n+1)(3n+4) #5)assume: 2+5+8+...+3n-1 = (1/2)n(3n+1) #5) prove: 3n+2 = (1/2)(n+1)(3n+4) - (1/2)n(3n+1) (1/2)*(n+1)*(3*n+4) - (1/2)*n*(3*n+1) ((1/2)*(n+1)*(3*n+4) - (1/2)*n*(3*n+1)).simplify() ((1/2)*(n+1)*(3*n+4) - (1/2)*n*(3*n+1)).simplify_trig() ((1/2)*(n+1)*(3*n+4) - (1/2)*n*(3*n+1)).simplify_radical() ((1/2)*(n+1)*(3*n+4) - (1/2)*n*(3*n+1)).simplify_rational() 

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