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00:00 - 00:59 | hello ka question is approved by the principle of Mathematical Induction in that n into n + 1 into 1 + 1 is divisible by 6 for all and along so definer principle statement that is free of any sort of energy equal to N into n + 1 into to 1 + 1 and we need to prove that that this statement is true for all natural number so first we will check that at any equals to 1 whether the statement is true or not for n = 21 P of X is equals to 1 into 1 + 1 + 1 will be 2 into 2 and + 1 this is 3 so this comes out to be sticks to as we know that sex is divisible by 6 hence |

01:00 - 01:59 | Tu so one that is at n = 21 this statement is true of one is true we assume that a statement is true for at an equal to M for any and equals to M so let P of be true so if your family is through what we get key of MS like what condition do we get from here is an end to end + 1 into 2 and + 1 so this is the statement if we get and as we are holding it through this will be equal to 6 cylinder because it is a multiple of 6 that is if three of them is true that means we of MS divisible by 6 so that means it is a multiple of 6 |

02:00 - 02:59 | use this condition to prove that P of M + 1 is true to what we need to provide us we need to prove that P of M + 1 is true to what is the statement that is what is P of M + 1 + 1 is N + 1 into 1 + 2 into 2 into m plus one that is to 1 + 3 digit need to manipulate the terms so that we can use this condition so what I am doing this I am X these two brackets that is the first to brackets and multiplying them so venom |

03:00 - 03:59 | what are get it m into n + 1 + 2 into 1 + 1 and I am breaking this 3 into 2 + 1 so what I'm taking commonest to 1 + 1 and taking the quantum and the second term is 2 and the reason why making this 12 + 1 is because we have this term in are in a the term which the condition which we have that is an equation when we have a square + 1 the way need to create that now we're just X square + 1 with these and these terms so on multiplying this what we get it to A + 1 into mm into m + 1 + 2 into 1 + 1 into 2 |

04:00 - 04:59 | plus one and again multiplying the two by the terms what do we get it to into km into m + 1 into 1 + 1 now we clearly see that these are a part of a recreation one so this take Lander and what I am doing is I'm taking to into n + 1 common from the second bracket so to into m plus one I am taking this is common and what left Behind s2m + 1 + m&a and leaving 4 into a + 1 as it is Poland to helpless Venice as it can be written as 6 Lambda to into m + 18 |

05:00 - 05:59 | 3M + 1 + 4 into m plus one now what we are gonna take Splendor Plus again taking to into m plus one common from these bracket Pro 2 into 1 + 1 we are taking this is a common what left Behind is 3M + 1 + 2 = 26 Lambda + 2 into 1 + 1 into what we can see that two plus minus 3 and we can take three years from 3 into a + 1 what we see 308 Texas coming from the entire term and what left Behind is Lambda + n + 1 whole square |

06:00 - 06:59 | so let this comment ke which prove that P of M + 1 is a multiple of 6 and hence proved that the statement p and is true for all natural numbers to finally what we can write s p and that is N into n + 1 into 2 and + 1 is divisible is divisible by 6 for all and belongs to natural number so we are prove that principle statement and complete the solution thank you for watching |