HSC Science (Computer Science) 11th Standard - Maharashtra State Board Question Bank Solutions

Find the sum to infinity of the following arithmetico - geometric sequence:

`1, -4/3, 7/9, -10/27 ...`

Find the sum `sum_("r" = 1)^"n" ("r" + 1)(2"r" - 1)`

Find `sum_("r" = 1)^"n"(3"r"^2 - 2"r" + 1)`

Find `sum_("r" = 1)^"n"((1 + 2 + 3  .... +  "r")/"r")`

Find `sum_("r" = 1)^"n" [(1^3 + 2^3 + .... +  "r"^3)/("r"("r" + 1))]`

Find the sum 5 × 7 + 9 × 11 + 13 × 15 + ... upto n terms

Find the sum 2² + 4² + 6² + 8² + ... upto n terms

Find (70² – 69²) + (68² – 67²) + (66² – 65²) + ... + (2² – 1²)

Find the sum 1 × 3 × 5 + 3 × 5 × 7 + 5 × 7 × 9 + ... + (2n – 1) (2n + 1) (2n + 3)

If `(1 xx 2 + 2 xx 3 + 3 xx 4 + 4 xx 5 + ...  "upto n terms")/(1 + 2 + 3 + 4 + ...  "upto n terms") = 100/3,` find n

If S₁, S₂ and S₃ are the sums of first n natural numbers, their squares and their cubes respectively then show that - 9S₂² = S₃ (1 + 8 S₁) 

Answer the following:

Find 2 + 22 + 222 + 2222 + ... upto n terms

Answer the following:

Find `sum_("r" = 1)^"n" (5"r"^2 + 4"r" - 3)`

Answer the following:

Find `sum_("r" = 1)^"n" "r"("r" - 3)("r" - 2)`

Answer the following:

Find `sum_("r" = 1)^"n" ((1^2 + 2^2 + 3^2 + ... + "r"^2)/(2"r" + 1))`

Answer the following:

Find `sum_("r" = 1)^"n" ((1^3 + 2^3 + 3^3 + ... "r"^3)/("r" + 1)^2)`

Answer the following:

Find 2 × 6 + 4 × 9 + 6 × 12 + ... upto n terms

Answer the following:

Find 2 × 5 × 8 + 4 × 7 × 10 + 6 × 9 × 12 + ... upto n terms

Answer the following:

Find `1^2/1 + (1^2 + 2^2)/2 + (1^2 + 2^2 + 3^2)/3 + ...` upto n terms

Answer the following:

Find 12² + 13² + 14² + 15² + ... 20²