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If 1+a+a^2+a^3+ .....a^n=(1+a)(1+a^2)(1...

If `1+a+a^2+a^3+ .....a^n=(1+a)(1+a^2)(1+a^4)`,then n is given by

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The sum to n terms of the series 1+2 (1+(1)/(n))+3 (1+(1)/(n))^(2)+ cdots is given by

Prove by PMI that 1.2+2.3+3.4+....+n(n+1)=((n)(n+1)(n+2))/(3),AA n in N

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1.2+2.3+3.4+.........+n(n+1)=(1)/(3)n(n+1)(n+3)