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Sigma 1 To Infinity 1 Plus A A Square R Factorial

sigma 1 to infinity (1+a+a2+...ar-1)/r! Solution: ∑r = 1∞ (1+a+a2+...ar-1)/r! = ∑r = 1∞ 1(ar-1)/(a-1)r! = (1/(a-1))[∑r = 1∞ ar/r! - ∑r = 1∞... View Article

Suppose A B And C Are In Ap And A2 B2 And C2 Are In Gp If A Less Than B Less Than C Then The Value Of A Is

Solution: Let a = x-d b = x c = x+d a+b+c = x-d+x+x+d = 3x = 3/2 ( Given a+b+c = 3/2) => x = 1/2 i.e b = 1/2 Also a2,b2,c2 are in... View Article

The Sum Of 02 Plus 022 Plus 0222 To N Terms Is Equal To

Solution: Given series 0.2 + 0.22 + 0.222 + ...to n => (2/10)+(22/100)+(222/1000)+....n terms = 2(0.1+0.11+0.111+... n terms) Multiply... View Article

Which Term Of The Series Root 2 2 By 3 2 Root 2 By 9 Is 16 2187

Solution: Given √2, 2/3, 2√2/9,... is 16/2187 This is a GP with a = √2 r = √2/3 The nth term of GP = arn-1 √2(√2/3)n-1 = 16/2187... View Article

The Sum Of First Three Terms Of A Gp Is 7 By 9 And Their Product Is 8 By 27 Find The Common Ratio Of The Series

Solution: Let a/r, a, ar be the first three terms of GP Given sum = 7/9 and product = -8/27 Product => (a/r)a(ar) = -8/27 a3 = -8/27 a... View Article

If A B And C Are Positive Numbers In A Gp Then The Roots Of The Quadratic Equation Log Are

If a, b and c are positive numbers in a GP, then the roots of the quadratic equation (loge a)x2 -(2 loge b)x+ (loge c)= 0 are Solution: Given... View Article

Consider An Infinite Geometric Series With First Term A And Common Ratio R If The Sum Is 4 And The Second Term Is 3 By 4 Then

Solution: Given sum of infinite geometric series = 4 a/(1-r) = 4 ..(i) Second term = 3/4 So ar = ¾ ..(ii) a = 3/4r Substitute a in (i)... View Article

If Ln A Plus C Ln A C Ln A 2b Plus C Are In Ap Then

Solution: Given ln(a + c), ln (a - c), ln (a - 2b + c) are in A.P 2 ln(c-a) = ln (a+c)+ln(a-2b+c) (c-a)2 = (a+c)(a-2b+c) (c2-2ac+a2) =... View Article

If X Y And Z In Ap Then 1 By Root X Plus Root Y Are In

Solution: Given x,y,z are in AP. y-x = z-y x-y = y-z Taking reciprocal 1/(x-y) = 1/(y-z) Rearranging we get 1/(√x-√y)(√x+√y) =... View Article

If A B And C Are In Ap Then Which One Of The Following Is Not True

Solution: Given a,b,c are in AP Check the options. If a2, b2, c2 are in AP, then b2-a2 = c2-b2 (b-a)(b+a) = (c-b)(c+a) Since (b-a = c-b... View Article

The Sum Of The Integers From 1 To 100 Which Are Divisible By 3 And 5 Is

Solution: LCM of 3 and 5 is 15. The numbers between 1 and 100 which are divisible by both 3 and 5 are 15, 30, 45, ..90 a = 15 an = 90 d =... View Article

The Number Log2 7 Is

Solution: Let x = log2 7 Then 2x = 7 (since logb(x) = y, then by = x) This is possible only for irrational number. Hence option (3) is the... View Article

Three Numbers Are In Ap Such That Their Sum Is 18 And Sum Of Their Squares Is 158 The Greatest Number Among Them Is

Solution: Let the numbers be x-d, x, x+d Sum = x-d+x+x+d = 18 3x = 18 x = 6 So numbers are 6-d, 6, 6+d. Sum of squares = (6-d)2+... View Article

Let A1 A2 A3 Be Terms Of An Ap If A1 Plus A2 Plus Ap Then A6 A21 Equals

Let a1, a2, a3,... be terms of an AP. If (a1+a2+...ap.)/(a1+a2+...aq) = p2/q2, p not equal to q, then a6/a21 equals (1) 7/2 (2) 2/7 (3) 11/41 (4)... View Article

Let Tr Be The Rth Term Of An Ap Whose First Term Is A And Common Difference Is D If For Some Positive Integers M N M Not Equal N

Solution: Let T1 = a, common difference = d Tm => a+(m-1)d = 1/n…(i) Tn => a+(n-1)d = 1/m…(ii) (i) - (ii) [(m-1)-(n-1)]d = (1/n)-(1/m)... View Article

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