Question

Solve using mathematical induction: 1+2+3+4.....n=n(n+1)/2

Answer 1

let n = k
sum k terms = k(k+1)/2
(k+1)th term = k+1
so sum k+ 1 terms = k(k+1)/2 + k+1
= [k(k+1) + 2(k+1)] / 2
= (k+1)(k+2) / 2
this is the sum of k terms where k is replaced by k + 1
therefore if the sum to k terms is correct then sum to k+1 terms is correct
the sum of 1 term = 1*2 / 2 = 1 which is correct so it must be true for 2,3,4 .... terms

thus the formula is true for n terms (any number of terms)