prove that f(x)=1+x+x2+x3+ +xn is equal to 1-xn/1-x - Maths - Limits and Derivatives

Question

prove that f(x)=1+x+x2+x3+ +xn is
equal to 1-xn/1-x

Rahul Raj · Accepted Answer

dear student

the above expression should be 1+x+x2+
+xn=1-xn+11-xwhich is the sum of terms in GPwe can prove by mathematical inductionfor n=11+x=1-x21-x=1+xfor n=n, assuming it is trfor n=n+1LHS=1+x+x2+
+xn+xn+1=1-xn+11-x+xn+1=1-xn+1+xn+1-xn+21-x=1-xn+21-xso true for n+1 also, the above expression is proved

regards

prove that f(x)=1+x+x2+x3+...+xn is equal to 1-xn/1-x

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