हिंदी
तमिलनाडु बोर्ड ऑफ सेकेंडरी एज्युकेशनएचएससी विज्ञान कक्षा ११

Choose the correct alternative:1 + 3 + 5 + 7 + · · · + 17 is equal to - Mathematics

Advertisements
Advertisements

प्रश्न

Choose the correct alternative:
1 + 3 + 5 + 7 + · · · + 17 is equal to

विकल्प

  • 101

  • 81

  • 71

  • 61

MCQ
Advertisements

उत्तर

81

shaalaa.com
Mathematical Induction
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 4: Combinatorics and Mathematical Induction - Exercise 4.5 [पृष्ठ १९८]

APPEARS IN

सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 11 TN Board
अध्याय 4 Combinatorics and Mathematical Induction
Exercise 4.5 | Q 25 | पृष्ठ १९८

संबंधित प्रश्न

By the principle of mathematical induction, prove the following:

1.2 + 2.3 + 3.4 + … + n(n + 1) = `(n(n + 1)(n + 2))/3` for all n ∈ N.


By the principle of mathematical induction, prove the following:

1 + 4 + 7 + ……. + (3n – 2) = `("n"(3"n" - 1))/2`  for all n ∈ N.


By the principle of mathematical induction, prove the following:

32n – 1 is divisible by 8, for all n ∈ N.


By the principle of mathematical induction, prove the following:

an – bn is divisible by a – b, for all n ∈ N.


By the principle of mathematical induction, prove the following:

52n – 1 is divisible by 24, for all n ∈ N.


By the principle of mathematical induction, prove the following:

2n > n, for all n ∈ N.


Prove that the sum of the first n non-zero even numbers is n2 + n


By the principle of Mathematical induction, prove that, for n ≥ 1
1.2 + 2.3 + 3.4 + ... + n.(n + 1) = `("n"("n" + 1)("n" + 2))/3`


Using the Mathematical induction, show that for any natural number n ≥ 2,
`(1 - 1/2^2)(1 - 1/3^2)(1 - 1/4^2) ... (1 - 1/"n"^2) = ("n" + 1)/2`


Using the Mathematical induction, show that for any natural number n ≥ 2,
`1/(1 + 2) + 1/(1 + 2 + 3) + 1/(1 +2 + 3 + 4) + .... + 1/(1 + 2 +  3 + ... + "n") = ("n" - 1)/("n" + 1)`


Using the Mathematical induction, show that for any natural number n,
`1/(2.5) + 1/(5.8) + 1/(8.11) + ... + 1/((3"n" - 1)(3"n" + 2)) = "n"/(6"n" + 4)`


By the principle of Mathematical induction, prove that, for n ≥ 1
`1^2 + 2^2 + 3^2 + ... + "n"^2 > "n"^2/3`


Use induction to prove that n3 − 7n + 3, is divisible by 3, for all natural numbers n


Use induction to prove that 5n+1 + 4 × 6n when divided by 20 leaves a remainder 9, for all natural numbers n


Prove that using the Mathematical induction
`sin(alpha) + sin (alpha + pi/6) + sin(alpha + (2pi)/6) + ... + sin(alpha + (("n" - 1)pi)/6) = (sin(alpha + (("n" - 1)pi)/12) xx sin(("n"pi)/12))/(sin (pi/12)`


Choose the correct alternative:
In 3 fingers, the number of ways four rings can be worn is · · · · · · · · · ways


Choose the correct alternative:
If `""^("a"^2 - "a")"C"_2 = ""^("a"^2 - "a")"C"_4` then the value of a is


Choose the correct alternative:
Everybody in a room shakes hands with everybody else. The total number of shake hands is 66. The number of persons in the room is ______


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×