Question

for all n is greater than 1 prove that 1 square + 2 square + 3 square + 4 square + n square is equal to n into n + 1 into 2 n + 1 upon 6 mathematical induction ke sath HAL Karen

Answer 1

Step-by-step explanation:

step 1 .

put n=1 ,n(n+1)(2n+1)/6

= 6/6 = 1

step 2 .let it is true for n=k

1²+2²+3³...........k²=k(k+1)(2k+1)/6------- eqn 1

step 3.

now we have to prove that it is also true for (k+1)

1²+2²+3³........k²+(k+1)²=(k+1)(k+2)(2k+3)/6

now

LHs= from eqn 1

k(k+1)(2k+1)/6 + (k+1)²

now solve this

(k+1) (2k²+7k+7)/6

(k+1)(k+2)(2k+3)/6

LHS. =Rhs

hence proved

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