1. using mathematical induction prove that n(n+1)(n+2) is divisible by 6 and following:

2. 3.6+6.9+9.12+....+3n(3n+3)=3n(n+1)(n+2)

3. (1-1/2)(1-1/3)(1-1/4)........(1-1/n+1)=1/n+1.

4. 1/1.2+1/2.3+1/3.5+......to n terms=n/n+1.

5. 1/3.6+1/6.9+1/9.12+.......+1/3n(3n+3)=n/9(n+1).

6. 1/1.3+1/3.5+1/5.7+........ to n terms=n/2n+1

Question

1. using mathematical induction prove that n(n+1)(n+2) is divisible by 6 and following:

2. 3.6+6.9+9.12+....+3n(3n+3)=3n(n+1)(n+2)

3. (1-1/2)(1-1/3)(1-1/4)........(1-1/n+1)=1/n+1.

4. 1/1.2+1/2.3+1/3.5+......to n terms=n/n+1.

5. 1/3.6+1/6.9+1/9.12+.......+1/3n(3n+3)=n/9(n+1).

6. 1/1.3+1/3.5+1/5.7+........ to n terms=n/2n+1

Nishant Vora · Answer

Hi student,
the method is
Mathematical Induction is a special way of proving things. It has only 2 steps:

Step 1. Show it is true for the first one
Step 2. Show that if any one is true then the next one is true

Then all are true

Thanks,
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