The value of -n-145 i n - i n -1 isHint- - t n -t m - t n - t mA- 0B- i -1C- iD- i -1

The correct option is D i 1 ∑_n=1^45 i^n + i^n+1 = ∑_n=1^45 i^n + ∑_n=1^45 i^n+1 = ( i + i^2 + i^3 + ................. + i^45 ) + ( i^2 + i^3 + ..... ...

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Byju's Answer

Standard XI

Mathematics

Multinomial Expansion

The value of ...

Question

The value of $\sum_{n = 1}^{45} i^{n} + i^{n + 1}$ is ____________

Hint: $\sum t_{n} + t_{m}$ = $\sum t_{n} + \sum t_{m}$

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i+1

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i-1

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Solution

The correct option is D
i-1

$\sum_{n = 1}^{45} i^{n} + i^{n + 1}$ = $\sum_{n = 1}^{45} i^{n} + \sum_{n = 1}^{45} i^{n + 1}$

= $(i + i^{2} + i^{3} + . . . . . . . . . . . . . . . . . + i^{45}) + (i^{2} + i^{3} + . . . . . . . . . . . . . . . . . . . + i^{46})$

= $i^{45} + i^{46}$ = $i + i^{2}$ = $i - 1$

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Similar questions

(a) T_n = n find (i) T_n+1 (ii) T _n−1

(b) If T_n = n² − 1 find (i) T_n−2 (ii) T_n+1

(d) In a sequence T_n= 5 − 3n find (i) T_n+1 (ii) T_n+2

In the expansion of (a+b)ⁿ, n Є N the middle term is given by

Q. If in an A.P.,

T_{m} = n, T_{n} = m

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d = - 1

If $T_{n} = n^{2} - 1$ , find (i) $T_{n - 1}$ (ii) $T_{n + 1}$

Q. In an AP,

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denotes

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and

t_{n} = \frac{1}{m}

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The value of ∑45n=1in+in+1 is ____________ Hint: ∑tn+tm = ∑tn+∑tm

The correct option is D i-1 ∑45n=1in+in+1 = ∑45n=1in+∑45n=1in+1 = (i+i2+i3+.................+i45)+(i2+i3+...................+i46) = i45+i46 = i+i2 = i−1

The value of $\sum_{n = 1}^{45} i^{n} + i^{n + 1}$ is ____________

Hint: $\sum t_{n} + t_{m}$ = $\sum t_{n} + \sum t_{m}$