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[8+3+6+10+......+((n-1)n)/(2)+(n(n+1))/(...

[8+3+6+10+......+((n-1)n)/(2)+(n(n+1))/(2)=],[[" 1."(n(n+1)(n+2))/(3),2,((n+1)(n+2))/(6)," 3."(n(n+1)(n+2))/(6)," 4."((n+2)(n+1))/(3)],[243+5+6+8+9+,2n" terms "-,4n+5],[1.3n^(2)+2n,,6,]]

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1+(n)/(2)+(n(n-1))/(2.4)+(n(n-1) (n-2))/(2.4.6)+…....=

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Prove that 5^(n) (1+(n)/(5) +(n(n-1))/(5*10) +(n(n-1)(n-2))/(5*10*15)+…oo)=3^(n) (1+(n)/(2)+(n(n+1))/(2*4)+(n(n+1)(n+2))/(2*4*6)+…oo)

1.2.3+2.3.4++n(n+1)(n+2)=(n(n+1)(n+2)(n+3))/(4)

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Prove that (.^(n)C_(1))/(2) + (.^(n)C_(3))/(4) + (.^(n)C_(5))/(6) + "…." = (2^(n) - 1)/(n+1) .

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