`(1+(1)/1)(1+(1)/(2))(1+(1)/(3))......(1+(1)/n)` `n(n+1)`

1.	`(1+(1)/1)(1+(1)/(2))(1+(1)/(3))......(1+(1)/n)` `n(n+1)`
Answer» Let `P(n): (1+1) (1+(1)/(2))(1+(1)/(3))......(1+(1)/(n)) =(n+1)` for n=1 `L.H.S. =1+1=2` `R.H.S. =1+1=2` `:. L.H.S. =R.H.S.` `rArr` P (n) is true for n=1 Let P (n) be true for n =K `:. P(k) : (1+1)(1+(1)/(2))(1+(1)/(3))......(1+(1)/(k)) =K+1` for n = K+1 `P(k+1) : (1+1)(1+(1)/(2))(1+(1)/(3))` ` ....(1+(1)/(k))(1+(1)/(K+1))` `=(k+1)(1+(1)/(K+1))` `=(k+1)((K+2)/(K+1))=K+2` `rArr` P(n) is also true for n= k+1 Hence from the principle of mathematical induction P (n) is true for all natural numbers n .

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