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Find the sum 1 × 3 × 5 + 3 × 5 × 7 + 5 × 7 × 9 + ... + (2n – 1) (2n + 1) (2n + 3)
Concept: undefined >> undefined
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
Concept: undefined >> undefined
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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)
Concept: undefined >> undefined
Answer the following:
Find 2 + 22 + 222 + 2222 + ... upto n terms
Concept: undefined >> undefined
Answer the following:
Find `sum_("r" = 1)^"n" (5"r"^2 + 4"r" - 3)`
Concept: undefined >> undefined
Answer the following:
Find `sum_("r" = 1)^"n" "r"("r" - 3)("r" - 2)`
Concept: undefined >> undefined
Answer the following:
Find `sum_("r" = 1)^"n" ((1^2 + 2^2 + 3^2 + ... + "r"^2)/(2"r" + 1))`
Concept: undefined >> undefined
Answer the following:
Find `sum_("r" = 1)^"n" ((1^3 + 2^3 + 3^3 + ... "r"^3)/("r" + 1)^2)`
Concept: undefined >> undefined
Answer the following:
Find 2 × 6 + 4 × 9 + 6 × 12 + ... upto n terms
Concept: undefined >> undefined
Answer the following:
Find 2 × 5 × 8 + 4 × 7 × 10 + 6 × 9 × 12 + ... upto n terms
Concept: undefined >> undefined
Answer the following:
Find `1^2/1 + (1^2 + 2^2)/2 + (1^2 + 2^2 + 3^2)/3 + ...` upto n terms
Concept: undefined >> undefined
Answer the following:
Find 122 + 132 + 142 + 152 + ... 202
Concept: undefined >> undefined
Answer the following:
If `(1 + 2 + 3 + 4 + 5 + ... "upto n terms")/(1 xx 2 + 2 xx3 + 3 xx 4 + 4 xx5 + ... "upto n terms") = 3/22` Find the value of n
Concept: undefined >> undefined
Answer the following:
Find (502 – 492) + (482 – 472) + (462 – 452) + ... + (22 – 12)
Concept: undefined >> undefined
Answer the following:
If `(1 xx 3 + 2 xx 5 + 3 xx 7 + ... "upto n terms")/(1^3 + 2^3 + 3^3 + ... "upto n terms") = 5/9`, find the value of n
Concept: undefined >> undefined
Answer the following:
If p, q, r are in G.P. and `"p"^(1/x) = "q"^(1/y) = "r"^(1/z)`, verify whether x, y, z are in A.P. or G.P. or neither.
Concept: undefined >> undefined
State, by writing first four terms, the expansion of the following, where |x| < 1
(1 + x)−4
Concept: undefined >> undefined
State, by writing first four terms, the expansion of the following, where |x| < 1
`(1 - x)^(1/3)`
Concept: undefined >> undefined
State, by writing first four terms, the expansion of the following, where |x| < 1
(1 – x2)–3
Concept: undefined >> undefined
State, by writing first four terms, the expansion of the following, where |x| < 1
`(1 + x)^(-1/5)`
Concept: undefined >> undefined
