how to use mathematical induction1+2+...........+n=n(n+1)/2

For using Mathematical induction. Check two conditions 1) when a statement is true for a natural numbern=k,then it will also be true for its successor,n=k+ 1;
and2) the statement is true forn= 1. If this two conditions are satisfied then the statement will be true for every natural numbern. For your case check (1). put n=k and n=(k+1) and try to prove it. Then for (2), put n=1 and check for LHS= RHS. If both are satisfied then the series is true for any natural number n.

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