Question

1+2+3+4+ _ _ + n = 1/2 * n(n+1) prove with mathematical induction
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Answer 1

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Answer 2

Answer:

Step-by-step explanation:

We have,

LHS = 1+2+3+4+.....+n

RHS = 1/2*n(n+1)

Let us assume n= 1 is true,

LHS = 1

RHS = 1/2*1(1+1)

= 1

So n= 1 is true.

Let us assume n = k is also true, so

LHS = 1+2+3+4+.....+k

RHS = 1/2*k(k+1)

1+2+3+4+.....+k = 1/2*k(k+1) ........ (1)

No we should prove n = k+1 is also true.

i.e.

LHS RHS

1+2+3+4+...+k+(k+1) = 1/2*(k+1) (k+2)

Let us substitute (1) in LHS,

i.e [1+2+3+4+.....+k = 1/2*k(k+1) ]

So,

1/2*k(k+1) + (k+1)

=> k+1 (1/2 *k + (1))

=> k+1 ( 1/2 *k + 2/2)

=> k+1 ( 1/2* (k+2))

=> 1/2 * (k+1) (k+2)

=> RHS