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Find the sum of first n natural numbers....

Find the sum of first n natural numbers.

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Find the sum of first 100 natural numbers.

If the sum of first n even natural numbers is equal to k times the sum of first n odd natural numbers, then k is equal to:

If P(n) is the statement that the sum of first n natural numbers is divisible by n +1, prove that P(2r) is true for all r = 1, 2, 3,...... .

If S_1 , S_2 , S_3 are the sum of first n natural numbers, their squares and their cubes, respectively, show that 9 S_2^2=S_3(1+8S_1) .

The sum of first 30 natural numbers is:

By the Principle of Mathematical Induction, prove the following for all n in N : 1+3+5+....... +(2n-1) =n^2 i.e. the sum of first » odd natural numbers is n^2 .

If P(n) is the statement “sum of first n natural numbers is divisible by n + 1", prove that P(r + 1) is true if P(r) is true.

Find the mean of first five natural numbers.

MODERN PUBLICATION-SEQUENCES AND SERIES-EXERCISE
  1. How many terms of the sequence -6,(-11)/2, -5,.... must be taken to ma...

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  2. Find the sum of the series : 72 + 70 + 68 +....+ 40?

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  3. Find the sum of first n natural numbers.

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  4. Find the sum of first 100 natural numbers.

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  5. Find the sum to n terms of the A.P. whose kth term is 5k + 1.

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  6. If the sum of n terms of an A.P. is (pn+qn^2), where p and g are const...

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  7. If the sum of a certain number of terms of the A.P. 25, 22, 19, .. . i...

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  8. Find the sum of 32 terms of an A.P. whose third term is 1 and the 6th ...

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  9. If the first term of an A.P. is 2 and the sum of the first five terms ...

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  10. If the first term of an A.P. is 2 and the sum of the first five terms ...

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  11. If the 12th term of an A.P. is -13 and the sum of the first four terms...

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  12. Show that the sum of n consecutive odd integers beginning with 1 equal...

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  13. Show that the sum of first n even numbers is equal to (1+1/n) times th...

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  14. Find the sum of odd integers from 1 to 2001. (A) 100200 (B) 1002001 (C...

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  15. Find the sum of all natural numbers between 99 and 1001 which are mult...

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  16. Find the sum of first hundred even natural numbers divisible by 5.

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  17. Find the sum of all integers between 50 and 500, which are divisible b...

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  18. Find the sum of all numbers between 200 and 400 which are divisible by...

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  19. How many terms are there in A.P. whose first and fifth terms are -14 a...

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  20. If the sum of the first n terms of a sequence is of the form An^2+ Bn,...

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