prove that : 1+2+3 .... +n = 1/2n(n+1) using mathematical induction.
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given that, 1+2+3+.....+n=n(n+1)/2
Let ,p(n)=1+2+3+.........+n=n(n+1)/2
P(1) :1=1,which is true.
Assume P(k) is true,
1+2+3+..........+k=k(k+1)/2
we want to check if P(k+1) is true, so let us find
1+2+3+.....+k+(k+1)= (1+2+3+.....+k)+(k+1)
=k(k+1)/2+(k+1), since P(k) is true
=(k+1)(k+2)/2
so, P(k+1) is true.
And so, by the principle of mathematical Induction, we know that P(n) is true for every
n £ N.
Let ,p(n)=1+2+3+.........+n=n(n+1)/2
P(1) :1=1,which is true.
Assume P(k) is true,
1+2+3+..........+k=k(k+1)/2
we want to check if P(k+1) is true, so let us find
1+2+3+.....+k+(k+1)= (1+2+3+.....+k)+(k+1)
=k(k+1)/2+(k+1), since P(k) is true
=(k+1)(k+2)/2
so, P(k+1) is true.
And so, by the principle of mathematical Induction, we know that P(n) is true for every
n £ N.
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