Series, and Probability

Question 1

nth term of an AP

Answer 1

an=a+(n-1)d

Question 2

2 formulas giving sum of first n terms in AP

Answer 2

Sn=n/2[2a+(n-1)d]
Or
Sn=n/2(first term+last term)

Question 3

What is an AP

Answer 3

Sequence where any term different from proceeding term by a constant term

Question 4

Constant term in AP is called

Answer 4

Common difference d

Question 5

What is a GP

Answer 5

Sequence where each tern is a constant multiple of the preceding term

Question 6

What is constant multiple in GP called

Answer 6

Common ratio r

Question 7

Formula for nth term in GP

Answer 7

an= a× r^n-1

Question 8

Sum of first n terms of GP

Answer 8

Sn=[a(r^n -1)]/r-1

Question 9

Convergence of a series in words:

Answer 9

If Sn is sum of first n terms of any series and if n is approaching infinity, and Sn exists and is finite the series is said to be convergent

Question 10

Convergence of a series in formula:

Answer 10

Sum to infinity= a/1-r If -1

Question 11

Expansion of (a+b)^n where n is a +ve integer

Answer 11

(a+b)^n=(a^n)+(nC1×a^n-1×b)+(nC2×a^n-2×b^2)+…b^n