n-1 - n(n-1) (n+1) Prove that t(t+1...
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n-1 - n(n-1) (n+1) Prove that t(t+1) = - ?, for all natural numbers n 2 2. t=1

11th - 12th Class
Maths
Solution
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( sum_{k=1}^{infty} t^{2}=1- ) ( 2 quad n z ) ( (n-1)(n-1+2)(2(n-1)+1) ) ( frac{6}{2}+frac{(n+1)(n) times 3}{2 times j} ) ( frac{(n-1)(n)}{6}+frac{(2 n-1)}{6} ) ( =frac{n(n-1)}{6}[2 n-1+3] ) ( =frac{n(n-1)}{6}(2 n+n)=frac{n(n-1)(n+1)}{3} )
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